I heard that Hindus believe in reincarnation but Buddhists in rebirth.
What is the difference between reincarnation and rebirth?
Not sure if a previous thread was posted on the subject.
First of all, let me clarify your question, in a slightly different wording: You are not really asking the difference betweeen reincarnation and rebirth; you are asking the difference between the Hindu and Buddhist beliefs regarding how life continues after death--whether or not there is such a difference, and if yes what it is. The question thus clarified is more or less equivalent to: If both Hindus and Buddhists believe in reincarnation or rebirth, then is there any difference between these beliefs? If yes, what are they?
Then, it follows immediately that the answer to the first part of the above question is a clear and affirmative "Yes", and this is so because the Hindus, together with people from many other traditions, believe in, or have implicitly assumed, an inherent, ever-lasting, and unchanging element in human life which is usually referred to as a soul or self; yet we know in Buddhism that this is not true. To the (enlightened) Buddhists, the continuation of life is like the flowing of a river or water, and a river flows not because there is an independent identity that is controlling or driving it, it is because the river is subject to the law of gravitation and perhaps other laws of Nature, or in other words, the flowing of a river from high altitude to low altitude is due to the difference in gravity potential along its path. The continuation of life actually works in a similar mechanism, and it is not controlled or driven by any indepemdent existence such as a soul, it is driven by ignorance and cravings, which serve as the equivalent of gravity potential in the flow of a river. Thus life without ignorance and cravings is like still water on a flat ground, and it is going to flow nowhere. And a life at this stage is claimed to be enlightened, or equivalently, to have gained the power to enter Nirvana. In short, the Hindus' belief (of reincarnation) is a wrong view based on an unjustified concept of a soul or self, while the Buddhist belief (of rebirth) is based on the right view of non-self.
So, what matters is not words or concepts themselves, since one can freely define them and these are usually context-dependent; what really matters is the message conveyed to others by these words or concepts or by the statement that is built upon these words or concepts. Thus answers to your question may vary depending on how one defines terms, but the message should be just the same.
Next, to understand the Buddhist concept of rebirth is not to simply take it at its face value; it is to comprehend it by deep reflection and vipassana meditation, and thus it is necessarily related to the cultivation of right views and therefore, to enlightenment itself.
Lastly, since the Hindu belief of reincarnation has already been rooted in the wrong view of a soul or self, we had better reserve the word rebirth for exclusive Buddhist use, and in this sense it means to be born again (and again) in which case no inherent, unchanging identity or ever-lasting soul is implied or assumed, just like the flow of a river or water where what sustains is a constantly changing identity subject to cetain laws of Nature with no external mysterious power ever in work or present.
There may be other differences between the Hindu and Buddhist beliefs regarding the continuation of life, but the above is believed to be some of the most important aspects. Again, to avoid confusion or misunderstanding, one first defines or clarifies words or concepts, and only after that he/she proceeds to answer the question.
A Short Note:
People in this forum may, quite often, give different answers to the same question being asked, and that's probably because they are at different stages on their way to Enlightenment. While it is often claimed that different answers to the same question have reasons to exist, one should also be aware that some of these answers are probably not justified, or in some extreme situations, they may lead to, or they themselves simply are, wrong views. And the standard answer, should it exist, would be the one that is based on personal enlightenment.
PS: When I have a chance, I may come back to give a more detailed answer to your earlier question of what the Buddhist concept of reality is and why it is an illusion, since to me, many, if not all, of the answers provided so far seem to have missed the essence of the issue.