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I suppose it depends upon your perspective, but—from the client end—incoming mail is handled by a POP3 or IMAP server, and outgoing mail by an SMTP server. The 'in' and 'out' here refer not to the directional flow from a single point, which happens for both server and client in a bidirectional manner, but rather to 'inside' and 'outside' your mail domain. Conventionally, server <---> server transactions are SMTP, and server <---> client transactions are either POP3 or IMAP.
In the case of AIM Mail, which is simply AOL web mail, it is the AOL servers which handle the mail transactions, not the AIM servers, which are apparently dedicated to handling instant messaging transactions. In fact, when you access AIM Mail on the web, the URL looks something like this:
http://d03.webmail.aol.com
Assuming that the required services are running on each domain, they could have chosen to do it either way, but they apparently decided that AIM Mail (possibly an unfortunately named product because of the suggestion that it is messaging and not mail) would run in the AOL domain, not the AIM domain.
I haven't tried to use AIM Mail through AIM servers - I just dug up what little documentation there was about using AIM Mail with other clients and applied it to Mail under OS X.
AOL has gone a little crazy with this AIM branding thing, even now offering a free AIM Phoneline: an inbound only, route to voicemail if not answered, and access from AIM Mail or AOL telephone service, with a legitimate prefix and telephone number in your US area code. Strange. But I might just get one - after all, it's free…