Then based on what you've said, they are aliases.
Aliases are harder to deal with when using Outlook because as far as Outlook
is concerned, they're the same address. Outlook doesn't have the ability to
selectively download based on receiving address. What you can do, though is
set up two mail profiles (either in separate Windows users or both in one
Windows user), have an account that's address-specific for each profile, set
that account to leave messages on the server, and have a rule that deletes
ALL messages except those addressed to the specific address matching the
account address. That should allow you to both use the same mailbox while
still keeping the mail separated by reciving address when it arrives in
Outlook.