Pre rendering means that you render out your animations before the game runs. Real time animations happen in-game, which takes up precious CPU resources. If you are planning to make a mobile application then Real time rendering is pretty muchg out of the question..
Frame by frame means that you are sitting there with Inkscape, Gimp or any other non-animation package and trying to manually draw each frame, pixel by pixel.
I have noticed a lot of really bad animation advice on these forums, and game making forums in general.
People are saying the proper way to make a torch is to make an emitter (not a c2 particle) and have it spraying hundreds of alpha mashed flames on the screen, rotating and scaling them, and changing the opacity and blend modes. Mixing it with a Particle to add to the effect.
Looks great, and it is fun to program, but it will totally suck the life out of your CPU. This is how a PROGRAMMER who does not know anything about art, or the actual game making process does things.
You should try to "fake" as much stuff as possible. Little animations like torch flames should be made before the game is ever run, with as few frames as possible.
Rotating and scaling things in real time, is the biggest mistake I have seen on these forums. Not from newbies either. I am seeing some really high level users wasting CPU power left and right.
You should only do things in real time, when there is absolutely no other way to fake it.