I shall dust off my "I used to be a sales and marketing director" badge off and throw in my own opinion.
Marketing is paid-for stuff that the publisher does, like booking ads (in trade and consumer press) and sending out review copies.
Promotion is the don't-pay-for-it stuff like book signings, talking at conventions (so yes, you can get paid to do your promoting), giving interviews, going on telly or radio, blogging and social networking. This is usually the responsibility of the author but publishers do get involved with this side of things (eg publishers' PR departments will quite often arrange those radio and TV appearances).
Sorting out distribution for the books is something that would come under a sales department's umbrella, I think.
All of these three areas have some overlap: different publishers have different rules. But that's a rough guide, and I hope it helps.