I think "freemium" is the most common option. For instance, landgrab.net (a Risk clone) offers a premium option that lets you play more than four games simultaneously, and gives you other features.
I paid.
I paid.
At least I guess we're talking about browser games? Because if web-based includes MMOs then of course it's different. (well a lot of those are freemiums too, but many aren't).
Oh and I myself have once paid for premium features on tribal wars and paid for my friends too, so make sure it's easy to buy stuff for other people, they like doing that :-)
Gifting is interesting, I first noticed it with reddit. If you don't mind me asking, why did you pay for your friends on Tribal Wars?
Why did I pay for my friends? Well some were not even friends. I was basically a leader of a "tribe" there and made an "invitation contest" (every member could invite people to the tribe, top 3 inviters would get the "premium points from me". But let's be honest, the true underlying reason is "oh look how cool I am, I gave you a gift", in fact that little contest of mine was somewhat a scam, I made sure the right people won :-)
But generally speaking browser games and MMOs are very different in almost all aspects. Revenue models might be getting similar but everything else is fundamentally different. I guess that doesn't need explanation.
As for the money making potential I think MMO market is definitely over-saturated, competition is very fierce and barriers to entry big.
Web browser market is very saturated too, but mainly with low quality stuff, as in it's no sooo hard to build something better. But the downside is that most games really struggle with profits there.