The system is mostly the same as it was in Borderlands 1: Beating playthrough one does nothing except unlock playthrough two ("True Vault Hunter Mode"), beating playthrough 2 scales enemies and rewards to your level, unlocking playthrough 3 (if you're level 50, I believe). Playthrough 3 is new and scales to your level from the start.
True Vault Hunter Mode (playthrough 2-2.5)
Playthrough 2 is unlocked simply by beating Playthrough 1, and is identical to playthrough 1 until completion except with higher level requirements, higher level enemies and generally harder enemies.
Once you beat playthrough two, enemies scale to within 3 levels of you; some weak enemies (like Skag Pups) may be level 48, most enemies will be level 49-51, bosses will often be level 52, and occasionally enemies will even be 53. This is known as "playthrough 2.5" as it was in Borderlands 1.
Loot scales to within a couple levels; most drops will be level 49 or 50. Quest rewards scale to your level too; this is why it's important not to start certain side quests until playthrough 2.5, otherwise you'll miss out on the highest level rewards. Side quests scale to when you start the mission so don't take them too early, if you want a level 50 reward, wait until you've finished the main quest. Of course if the reward is green, you can go ahead and do it because the reward is junk anyway.
Note, without the UVHM DLC that it's still important to cap out your level, not just get to playthrough 2.5 before getting rewards, but as of right now the max level without the UVHM DLC is still 50, and it's hard not to be level 50 by the time you complete the second playthrough.
Ultimate Vault Hunter Mode (playthrough 3)
As of a patch April 2013, there is also now an Ultimate Vault Hunter Mode or playthrough 3, which is scaled to your level and much harder. It's mostly explained in these patch notes and this explanation:
- Ultimate Vault Hunter Mode is unlocked for a character once they have completed the main story missions in True Vault Hunter Mode and reached level 50.
- Unlike other playthroughs, Ultimate Vault Hunter Mode can be replayed multiple times with players able to reset their overall mission progress at any time from the Main Menu.
- No more tutorial missions -- characters in Ultimate Vault Hunter Mode begin in Southern Shelf with the "Cleaning Up the Berg" mission.
- While playing in Ultimate Vault Hunter Mode, enemies and bosses will scale according to the player's current level or, if playing with others, the highest-level player in that party.
-Gameplay changes in UVHM:
- Enemy health generally increased 4x.
- Enemies now have a moderate amount of health regeneration.
- Increased duration of slag damage multiplier effect.
- Upped the damage that slagged enemies take from 2x to 3x.
- Weapon swap speed increased to better facilitate slag use.
- Enemies now more likely to drop ammo.
- Loot Midgets are now "Legendary Loot Midgets" that can drop Legendary and other top-tier gear.
- Powerful new “Ancient” E-Tech relics and rare Pearlscent-grade weapons can be picked up in Ultimate Vault Hunter Mode.
Generally speaking, enemies are harder, have much more health, slag is much more effective, rare drops are increased and certain new E-Tech relics and Pearlescent (cyan colored) equips are avalible only in UVHM. The E-tech relics and Pearlescents are only availible in UVHM for people with the Ultimate Vault Hunter Upgrade pack ($5 DLC, included for free with the Season Pass).
Note that due to the increased difficulty and increased efficacy of Slag, UVHM is particularly suited to co-op play. Just like in "raid" boss fights, a Siren with Res is always useful.
To my knowledge there's no "playthrough 3.5" since the ".5" was always about enemies/loot that scale to your level. Playthrough 3 scales from the start so there's no extra post-playthrough for scaling.
Best Answer
This isn't anything like the stupid restrictive classes in Mass Effect - they're not limiting like that. Anyone can be pretty devastating with any gun, but the skills are awesomeness on top.
Each of the characters has three branches to the skill trees, which seem to always be of roughly the same types:
The left branch offers some good early bonuses and is easy (or at least obvious how) to master. For instance Maya gets more shields and gun damage, Zero gets more sniper damage.
The middle branch benefits co-up (healing your teammates, allowing them to do more damage, etc). For instance Maya gets team healing, Zero can tag enemies to do them more damage.
The right branch is tougher to master but offers some serious klout at the top. For instance Maya gets more elemental damage (useless until about level 15 when elemental guns start to be plentiful enough, but devastating at level 50) and Zero gets insane melee damage and re-cloaks with melee kills.
Respecs are cheap and respec stations in the hub areas of the main game and DLC, so you can tweak your characters a lot. At level 5-20 you find yourself on the left a lot, but the real fun comes with lots of playing around and respecs later on.
The massive differences come at higher levels, and it really becomes about using the right weapons for the playing style.
You can focus on DPS for any of the characters, but it will work in different ways: Maya gets per-shot elemental bonuses (making SMGs/Shotguns do insane damage) while Salavdor gets never reloading and ammo regen (making Vladof spin-up assult rifles devastating) and so on.
All the high level powers are pretty cool.
Axton is the easiest to master and the most conventional - he's a lot like Roland in BL1. His turrets get pretty awesome and it's essential to have at least one Axton on your team for kiting some of the level 50 boss raids.
Salvador is the next easiest: he's all about spitting loads of ammo but he can also become pretty tank-y. He can keep spewing lead even when fighting for his life which can be a good survival tactic.
Zero can be either sniper or melee, you kind of have to pick one or the other. I found levels 1-20 as a sniper and then 20+ ninja everything :-) With the right gun and an Amp shield Zero can take down or nearly wipe out most enemies in a single head shot.
Maya is all about elemental damage - if you understand how to use that, what enemies are weak to it, which ones resist it and how it stacks then she does (by far) the highest DPS, possibly even overpowered. It can take some getting used to, and you find that you need one of each elemental weapon type to hand all the time. Maya is also essential for some co-op with her healing tree and is the only character that can remote-heal others.
I'm not that used to Gaige yet, but I think her skill (by default) is a little like Axton's - the real fun is in her 'right' tree: Anarchy. By changing the reload dynamic it makes it tough to master (you'll swear because you accidentally hit reload instead of open chest because you were slightly too far away).
In short: whoever you pick you'll find something to enjoy in the playing style.