Mail delivery

[Zr40]

I have two email addresses, of which one is an alias. If I retrieve my mail, I get it for both addresses.
I've installed postfix to see if I could figure it out, but I couldn't.
What do I need to put in the config file (and/or do I need other packages) to get the mail for the primary address delivered to my pc, and the other mail to another pc?
BTW, I don't want to use postfix (or any local mail server) for mail sending.