Qual é a diferença entre keep e keep up?

"Keep" is synonymous with continuing to (do something) and it's followed by a verb. An example would be "keep doing a good job". "Keep up" can be used in the same context however you can't use a verb right after. In this case it's usually followed by a adjective + noun structure (Keep up the good job.)

Another usage for keeping up is when you refer to remaining close to someone at a particular task, as far as being able to do it equally well and effective. For example imagine this conversation:

Hey, wanna go for a run?
Yeah, but don't go too fast or I won't be able to keep up with you. (you can translate it as "acompanhar").

Another example of a sentence in which it can be used: I have trouble keeping up with my co-workers. They do things way too fast and it gets me overwhelmed.

Also another usage for "keep" is claiming something as your won or being offered to have it, often in a context where you were borrowing an item, then when you give it back to whoever owned it they say "Keep it" as in they don't mind letting you have it permanently and won't be taking it back.

A few other contexts are "manter" as in "some people keep their hands on their chest when they sing their nation's national anthem" or "You must keep your skin moisturized for optimal skin quality". Also when you talk about the place in which you stash a particular household item or whatever else it may be. Example: "I keep my shoes in my closet." In this case the verb can be translated as "guardar".

Well there you go, I hope I've made it all clear. Not sure I've covered everything there is to it, though. Someone else might come in and add some other context I might have forgotten.