if I change my password on two different servers, using the same string but the encrypted password in /etc/passwd look different.
If I copy an entry from one /etc/password to the other server. I can still log in to both servers using the same password. Only now both /etc/passwd entries are identical.
How is this possible?
It's the way encryption works to protect passwords, Here is one link to some info:
docstore.mik.ua/orelly/other/puis3rd/0596003234_puis3-chp-4-sect-3.html
They don't want people to be able to compare hashes like that. Otherwise, if an attacker got to the hashes, they could compare it to a list of known hashes -- which would speed up password bruteforcing tremendously.
In short, they mutate (salt) it a little to prevent people from doing exactly what you tried to do just now. 