I am currently writing a paper on non-standard models of Peano arithmetic and I am having trouble finding references or information that discuss the relative sizes of how many models of Peano arithmetic there are in the standard and the non-standard cases.

I see it quoted all over the place that, "It is familiar that there are continuum-many pairwise non-isomorphic countable models of $\mathsf{PA}$". From this I take it that there are $\mathcal{c}$-many ($\aleph$-many) non-standard models of Peano arithmetic. Where can I find a proof of this fact? How many models of Peano arithmetic are there that are isomorphic to the standard model?

Thank you!