What's the difference between a bijection and an isomorphism? [duplicate]

I don't understand what the difference is between a bijection and an isomorphism. They seem to both just be a invertible mapping.

Is the set of all bijections a subset of isomorphisms? Or vice versa? What is the difference and can you show me an example of one that is not the other?

Thanks.

If you are talking just about sets, with no structure, the two concepts are identical. Usually the term "isomorphism" is used when there is some additional structure on the set. For example, if the sets are groups, then an isomorphism is a bijection that preserves the operation in the groups: $\varphi(ab) = \varphi(a)\varphi(b)$. As another example, if the sets are vector spaces, then an isomorphism is a bijection that preserves vector addition and scalar multiplication.

The answer is "vice versa." An isomorphism is a structure-preserving bijection. The specific meaning of "structure" will vary, depending on the context.