Toons are the main protagonists and playable characters of the game, they're your basic "make a character here" avatars.
The Toons are the main inhabitants of Toontown, in a similar vein as traditional Disney cartoon or Roger Rabbit anthro characters. They mainly rival the games main enemies, The Cogs, being the exact opposites of them (goofy and toony). Thus they must make use of the in-game "attacks" known as gags to defeat The Cogs.
Originally in TTO, there were only 6 animal species available to use, the dog, cat, duck, mouse, rabbit and horse toons. However 3 more species were added in via a popularity vote out of 6 (the bear, the pig and monkey toons). In TTO most of the species were free to use apart from bear, horse and monkey toons but since the arrival of fan servers and obviously not being able to paywall any of these features, all of these species have been made free to pick and choose now alongside new animal species added due to popularity or similar votes such as the crocodile/alligator, deer and in TTCC's case, beaver, fox, bat, raccoon, kiwi, kangaroo, koala, armadillo and turkey toons.
Gags are the in game "weapons"/items used in battle to combat the cogs, in the original TTO there were only 6 gags to use however with the change of battle mechanics, two more gags that would work with two of the pre-existing gags would be added.
I'm working my way to getting all gags to unlock but my favourite gag so far has to be throw, I use it way too much especially in comparison to other gags I have to desperately level up but it's a good old reliable attack! Especially when prestigued which I will be sad to not have since I'm going for an all gag build.