I guess the biggest differences are that Battlefield 3 costs a whole lot more than a normal game if you want to play competitively, the progression system, origin & the battlelog, no modding, no LAN or bot matches, and the way (mostly infantry) combat feels.
So (for the US any way) the base game costs roughly $30, now it's a complete and finished game but to play competitively you will need to spend another $50 for all four of its expansions.
Now if you just buy the base game and sort the server browser so it's just the base maps, you will still fight against/with people who have weapons you can't own; That might not sound very major, but those people will always have an edge over you even if the new weapons were perfectly balanced (which they aren't) due to the additional options they have.
Ever since Battlefield 2, the Battlefield series has had a progression system, this may or may not be a bad thing to you. In this particular game it's a standard progression system for the most part:
get xp for playing
get new weapons/gear by leveling
though for the vehicles many of the new things you unlock are straight upgrades in the beginning ex. jets start without a secondary weapon nor flares to evade lock-on missiles.
To play Battlefield 3 you need to install Origin and the battlelog plugin for your browser. Origin is EA's answer to Steam, if you have ever used Steam before it's much like that. The only problem with the browser plugin is that you have to log in and select the server you wish to play on from your browser, you also can't change any options (video, controls, audio) until you're in a match.
In previous Battlefield games excluding the Bad Company line, it was possible and fairly easy to mod the games see:
Project Reality Battlefield 1918, where in Battlefield 3 it's a bannable offense to use something as simple as a
mod that changes the tint of the maps.
There is no LAN or bot match mode where you can mess around/learn the vehicles and maps, so you are forced to learn as you go.
The most important change to the game itself is way infantry combat works, it's either very close quarters and like a two way meat-grinder, or who ever sees the other person first shoots and wins. It's more practical to use a vehicle like in the other Battlefield games when possible, but vehicles are usually a means of transport due to how quickly they get destroyed, excluding jets, helicopters, anti-air tank, and sometimes tank.
Sorry for the long post, but I wanted to give a relatively detailed list.