I was wondering if someone could explain to me how the Galois Field GF(p^n) compares to the ring Z/(p^n)Z i.e. the ring of integers modulo p^n, where p is a prime and n is any integer.

I know that the first one is a field while the second one isn't. However, they seem to have equal number of elements. I just want an intuitive comparison of these two.

I wish to know this because GF(p) and Z/pZ seem to be exactly the same structures!