Q: How are Buddhism and Hinduism the same, and how do they differ--specifically in relationship to the four noble truths of Buddhism?
A: The Four Noble Truths of Buddhism and Vedantic Hinduism

Let me begin by defining the terms before expanding on the concepts and addressing this very intriguing question. The four noble truths are the fundamental concepts of Buddhism, which are attributed to Buddha himself. They can be summarized this way:
1. To live is to suffer.
2. Suffering is caused by desire.
3. To eliminate suffering, one must eliminate desire.
4. One can eliminate desire by following the noble eight-fold path.
Vedantic Hinduism is the monistic form of Hinduism according to which the only true reality is Brahman and one can find one’s true identity as Brahman deep within one’s true self, called Atman.
Now let me elaborate on both of these segments of the question. First, let us look a little more at the four noble truths. In Buddhist teaching, when the Buddha attained his enlightenment, he attempted to find a middle way between the life of luxury that he had led as a young man and the extreme asceticism he pursued in the time right before his new awareness. In a nutshell, what his teaching came down to was that one should neither cling to the world nor attempt to escape from it through leading an excessively harsh life, but one can be released from this world by establishing an attitude of disconnectedness from it. The four noble truths elaborate on this position.
The first statement summarizes a widely held Indian understanding of life, namely that the very fact of one’s existence brings about suffering. It is inevitable that, as long as one is alive in the world, one winds up suffering. Suffering (dukha) is both direct (pain, old age, death) and indirect (not attaining a spiritual escape). This awareness of suffering, though publicized in the Buddha’s teachings, is really at the heart of most Indian philosophies. There may be variations on how the suffering is described in detail, and there definitely will be differences in how this suffering is explained, as well as what escape route is proposed, but the fundamental conviction that one’s very existence within the universe is the root of the human dilemma is a pan-Indian notion. This starting point also applies to Vedantic thought. In this form of Hinduism, the biggest problem besetting any human being is that we are not only entrapped in a finite and ultimately unreal world, but that we are even ignorant of that fact, and consequently, we try to find all kinds of ways of shaking off our situation, which is only going to make things worse.
The second of the four noble truths establishes the basic cause for suffering, namely that we are beings beset by desire. The word (tanha) that has traditionally been translated as “desire,” goes far beyond the ordinary English meaning of “desire.” It is not so much a matter of “wanting something” (after all, one “wants” nirvana), but of being totally attached to something or clinging to something. Just to mention some of the core “desires,” as an average human being I take my health, my youth, my prosperity, my relationships with family and lovers, or my daily food, clothing and shelter as non-negotiable entitlements. I want them, I feel that I need them, and I’m going to spend a life time finding them. No wonder that I’m going to suffer because the very nature of the universe decrees that I will not attain my goals. Everything in the world is fleeting, constantly changing, and, in the final analysis, just a set of interconnected illusions. Thus the more I cling to my existence in this sham world, the more likely I’m going to be to be disappointed and walk away very unhappy.
Again, Vedantic Hinduism is very close in its teaching to Buddhism on this point. It also supports the idea that we are living in a world of less than ultimate reality (maya), and it also warns us that treating the world as though it were real is the main problem of human beings. This is one of the ways in which Vedantic Hinduism sets itself apart from other forms of Hinduism. All schools of Hinduism (and, indeed, is this not true of most religions to some extent?) declare that this reality is not all there is, that there is, in fact, a higher reality, but in many schools of Hinduism the reality from which we must escape is not purely an illusion as it is in Vedanta and in Buddhism.
The third noble truth, then, gives us the logical conclusion to the first two: if life is suffering, and we want to escape suffering, and suffering is caused by attachment, then there is one obvious way of eliminating suffering, namely by ridding ourselves of attachment. Give it up! As long as you cling to life, health, love, food, youth and all those things that will bring you pleasure by having them and pain by not having them, the pain is going to be inevitable because you definitely, absolutely, guaranteed not have them. Old age, enfeeblement, the death of others, not to mention your own death, and the corruption of your body are inevitable. So, the Buddha’s message runs, stop pretending that they are not! Stop looking for physical ways or religious beliefs that will deny this fundamental reality. In order to find true release from the suffering of the world, you need to quit holding on the world, your health, your relationships, your physical comforts, yes, even your own existence as though they were what mattered in life.
To pick one simple example, if old age brings about suffering, and we all know that old age is inevitable, what a silly idea it is to try to attain happiness by delaying old age! At best we are simply postponing the inevitable, but more likely we are going to spend a large part of our lives in frustration, trying to escape from something that is guaranteed escape-proof. Similarly, the Buddha, who was himself a very handsome man of unequaled skill in archery among his peers, the husband of a beautiful woman, and the father of an exceptional child, looked at the world around him and at himself and saw that all of one’s physical life was nothing more than a temporary station on the way to becoming a rotten, stinking, decaying corpse. Not a pleasant thought, to say the least, but—the Buddha argued—why would anyone think that spiritual release can be found by cultivating one’s “pre-corpse” body? We must let it go.
Since we already said that Vedantic Hinduism agrees in the main with the first and second noble truths, it follows that it must also agree with the basic stipulation of the third truth. That is to say, if life is suffering and if suffering is caused by attachment to an illusionary world, then, obviously, the way to eliminate suffering is by foregoing attachment to this world. However, the somewhat bleak picture I have drawn of the Buddha’s viewpoint above, which is generally not stressed in later schools of Buddhism, would not be found in Vedanta. The emphasis of Vedanta is not one of detaching from this life as reattaching to the higher reality of Brahman. It is here that the difference between Buddhism and Hinduism already becomes stark. For (traditional schools of) Buddhism there simply is no absolute reality that one can stake one’s existence on, and the most serious mistake we all make is when we try to find such a reality and make ourselves dependent on it. By contrast, Vedanta contends that there is one and only one true reality, and until we have found it we will continue to be tied to this world. Thus, even though both sides agree that we must become liberated from the bondage of thinking that this world is reality, Buddhism counsels us to step forward into the realization that there is no absolute reality to takes its place, while Vedanta directs us to the absolute reality of Brahman.
The fourth point becomes very specific to Buddhism. It informs us that the way to suppress our attachment to this world is by following the noble eight-fold path. These eight concepts are called the “path” toward liberation, but it might be best to understand them as the goals that a Buddhist monk, someone who has devoted his entire life to this quest, is going to strive for. The eight principles are: 1) right view—to understand reality correctly; 2) right intention—to resolve to pursue the path toward enlightenment to the end; 3) right speech—to limit one’s speech to those utterance that will achieve liberation; 4) right action—to observe the physical prohibitions placed on a monk (not to harm any living being, not to touch gold or silver, not to eat after noon, etc.); 5) right livelihood—to devote one’s life to the search for enlightenment as a monk; 6) right effort—to put all of one’s energies into this task; 7) right meditation—to follow the correct patterns of thought that will lead to release (often a rigidly prescribed scheme); and 8) right concentration—to learn to focus one’s mind, for it is ultimately mental power that overcomes attachment to the world.
Insofar as the eight-fold path describes a specifically Buddhist way of life, Vedantic Hinduism clearly parts ways, but even then similarities remain. The Vedantic ideal is the sannyasin, a person who has broken completely with his previous life, such as family, occupation, or social standing and has withdrawn into complete isolation, perhaps even living alone in the forest or traveling from village to village, all the while seeking his identity with Brahman through meditation. By the very nature of the role the sannyasin plays, he is not governed by traditional rules, and so there is a clear difference to the Buddhist monk (bikhu). Nonetheless, the two certainly share the goal of devoting their entire lives to the quest for salvation.
And so we see that Vedantic Hinduism and the four noble truths of Buddhism have a certain amount of commonality. Their setting in Indian thought, with its emphasis on the denial of the ultimacy of the world and the need to escape from its fetters, clearly manifests itself in both contexts. However, there are also important distinctions, such as the Buddhist denial of any absolute reality and the Vedantic affirmation of Brahman as the foundation reality.
Even though some writers have wanted to carry this idea even further and show in the name of a “perennial philosophy” that all religions, including Christianity, fit into this pattern, such efforts are not successful. Christianity does teach that we should not put our hope into material things and the present world, to be sure, but it does not teach that the universe is an illusion from which we need to liberate ourselves. According to the Bible, the physical world was created by God and declared to be good by him. The human dilemma is not that we live in the finite world, but that we have disobeyed the God who created the physical world and us as finite beings. We are not sinful because we are finite, but we are finite and sinful. Sin is not a matter of being finite, but of existing in a state of alienation from God. Thus, escaping from our finitude, even if such a thing were possible, would not solve the deeper problem of being sinful. What Christianity proclaims is that we can be in a right relationship with the creator, thanks to the work of Jesus Christ, and that then our existence in the finite world can become meaningful. The person who has found his or her true relationship to God is no longer ensnared by thinking that the finite world is all there is, but it would be putting the cart before the horse to think that simply by denying the world we can accomplish this goal. Such liberation can be found by placing one’s faith in Jesus Christ.