Suppose that $K_1$ and $K_2$ are two triangulations of the same polyhedron. Are the chain groups $C_p(K_1)$ and $C_P(K_2)$ isomorphic?
my Idea is that they won't be necessarily ,because I think the generators will change if we change the way that we triangulate with simplexes.
please make me correct if I am wrong and tell me if I am right,thank you very much.
No at all. Two triangulations may well have, for example, different number of simplicies in some dimension.
For example, you can easily find for each $n\geq1$ a triangulation of the interval $[0,1]$, each of which has $n+1$ vertices and $n$ $1$-simplices.
Now, even if the two triangulations have exactly the same number of $p$-simplices for all $p$, the corresponding complexes may well be different. You should try to find an example of this: look for triangulations of a triangle.