I don't know a whole lot about this stuff but I'll take a stab at it.
SALES AND TRADING -- The sales guys and the traders work closely together. The sales guys are typically strong with soft-skills, so they can entertain clients and do the smooth talking, while the traders are more quant-oriented, although many traders insist a monkey could do their job.
95% of people who call themselves traders are "market-makers," nothing too glamorous, you're just following a strategy set by the bank, and you manage your inventory buying and selling securities all day making a profit on the spread.
The other 5% are proprietary traders. These are basically speculators, people who are trusted by the bank to turn buckets of cash into more buckets of cash. These jobs are hard to come by, so much so that it's probably not realistic to think you can land one of these jobs without first working as a marketmaker.
ASSET MANAGEMENT
Sell-side means you're working for a bank that is trying to sell securities to people/institutions. The sell-side equity analysts analyze equities and find a way to say, "This is a great stock." Obviously there's no conflict of interest here, it's like when a used car salesman gives you his objective opinion on how great his '84 Pinto is, he's really just being straightforward and honest.
Buy-side means you work for an institution that is not selling, but purchasing for the purpose of investing. So a hedge fund or a mutual fund management company like Fidelity. The difference here is that rather than analyzing equities (or bonds or whatever) and cranking out reports that say how awesome these instruments are, you are interested in finding out what's really going on because your job is to get the biggest returns possible with a set amount of risk, so you want to know everything about your investments possible.
So the big difference between sell-side and buy-side is that the purpose of your analysis is different. I think generally speaking compensation is roughly equivalent when you start out, but as you move up it's probably better to be working buy-side. It's also thought of as more prestigious because everyone wants to work at hedge funds and have the opportunity to switch jobs within an organization like that.
So like I said, this is just my cursory understanding of this stuff, no doubt there are better explanations out there.