Correct grammatical use of mogę and mógłbym?

I am currently learning polish and right now when I learn phrases I feel like I am memorizing them and not learning proper grammar. For instance, "Czy mogę poprosić menu?" and "Czy mógłbym poprosić trochę wody?" both translate to May I have a menu and May I have some water?

What is the difference between mogę, mógłbym, and other variations? Or is there a difference?

It means the same basically. Not much difference. I'm not an expert, but for me it's like mogę?=can I? and mógłbym=I wish I can.

Still, better not to dig up too deep in Polish language - it may only arise confusion ;)

mogę = may I, can I?

Mogę poprosić o menu? = May I ask for the menu?

Mógłbym = would I be able to? The use of the conditional here just adds an additional note of politeness.

Mógłbym poprosić o menu? = Would I be able to ask for the menu? More colloquially: "Could I possibly have the menu?"