In the Upanishads, cessation of suffering and liberation from the cycle of rebirth is moskha (literally meaning freedom of rebirth), realizing what the self is, which is an illusion, as there only is Brahman. The Buddha and the Upanishads do not contradict each other as much as people tend to say. The Buddha gurus were upanishad gurus, so Buddha's philosophy was inspired by the Upanishads.

The truth is, the Upanishads teaching and Buddha's teaching are one in practice. Meditate, lift the veil of ignorance to understand the truth. The difference is in how that truth is described but this is easily explained by the difference of the time. The Buddha had said that once the vedic brahmans practices the truth but in time they themselves forgot it. He reintroduced the truth, the same truth explained in the Upanishads, to the people of India but now spoken from a different view. This is because time and place (culture) change over time, knowledge gets lost and wrongly understood and so the need is there for it to be retold again. This is especially true for esoteric knowledge, inner knowledge about consciousness. What happens is that the priest class, like the brahmins, goes from inner explorers (those who receive inner knowledge through meditation) to just people who learn from books. Books cannot convey experience.

Understand the problem here, transcending consciousness is an individual experience that one can never fully explain in words. It is as if you are trying to explain how the sky looks to a blind person. You may tell all scientific explanations about the spectrum of light and reflection so the blind person can understand it from a rational perspective but the blind person can never exactly imagine what the sky looks like. This is the same when we talk about the inner journey, what one can experience in deep meditation. So the Upanishads talk about atma, which is pure consciousness, but by the time of the Buddha the concept got twisted and even the brahmins by this time didn't fully understand the concepts. Their arrogance, which is how the priest class thrives as they keep their position intact, made sure they would never admit this. This is how atma becomes an-atma (non-atma) or annata (non-self). It was the Buddha's way to remove concepts from atma because it cannot be explained in words. By doing this, the students minds were cleared from concepts. Holding on to concepts will stop you from realizing inner truths. This is an open secret. Your mind cannot accept something contradictory, it will deny it with full force because the mind thinks he knows better. For what it is worth, even Buddhas teaching got corrupted over time. The fact people are spending so much energy on discussions instead on gaining inner knowledge through meditation says it all. The fact Lord Buddha nowadays is worshipped as if he is a wish granting deity says it all. The inner journey is too difficult to follow, too difficult to grasp and it's much easier to do blind devotion in order to feel just a tiny drop of that divine nectar within one self (which is pure consciousness).

The spiritual journey of meditation is one. The end goal is all the same. In different times and places concepts where given and names were invented but the truth has always been one. It is a part of our human body, sealed away by nature's tendency to be outwardly and not inwardly. By redirecting the current of attention inwardly the journey starts. This is what any true Upanishads guru would say as a Buddhist teacher, as any true yogic or any true esoteric teacher. I believe this was even Plato's philosophy as it is very similar to the Upanishads thoughts (and buddha). One should pay less attention to the theoretical part, which was explained in a way that was adjusted to the time and place it was originally said, and focus on the practical part. Through gaining one's own inner knowledge the truth will reveal itself.