How can you tell the difference between human and animal bones?
Biochemically, you can't.
At the tissue level - that is, individual cells and the matrix the cells live in - human bones are identical to animal bones.
That said, the bones are different shapes depending on what species they came from. So you could can classify them as human or non-human that way. Also, you could extract DNA from the cells inside the bones, sequence it, and map the results back onto to samples taken from humans or non-human species the bones might have come from.