[vasyasvc]

So did the Buddha teach and believe in rebirth then?

The Buddha taught about rebirth and references to it can be found in many suttas. I think that most Buddhists probably interpret it literally and some prefer to interpret it as being used primarily as a morality teaching, others as 'moment to moment' rebirth looked at in the context of the same lifetime and so on.

As far as the word 'reincarnation' is concerned, that comes from Tibetan Buddhism and 'reincarnate' lamas. When a lama dies it is believed that his 'reincarnation' can be found and will continue in his place at a monastery or wherever, after being re-taught the necessary teachings from as a small child onwards.

Personally I don't hold a position about rebirth one way or the other because its not relevant to my practice in the here and now.