abstract algebra – Ring of Endomorphism over $mathbb{Z}_n$

I must have some definition problem which I can’t put my finger on:
When defining homomorphism of rings $ f :R mapsto S$, we require:
Now I have question asks to prove that End($mathbb{Z}_n$) isomorphic to $mathbb{Z}_n$. If every endomorphism $f$ must send 1 to itself, and preserve sum, how can I get 2 different enomorphisms?