[subject] + [verb] + [noun] + 还是 + [noun]?
[subject] + [verb phrase] + 还是 + [verb phrase]?
[subject] + 是 + [noun] + 还是 + [noun]?
还是 between two options turns the sentence into a question that asks the listener to pick one. The answer is one of the options, so there is no 吗.
The options can be nouns, verb phrases or whole clauses. Repeating the verb in the second option is common.
A verb and its negative make a blunt yes-or-no choice.
或者 also means "or", but it lists options in a statement and asks for no choice. English uses "or" for both, so learners reach for 或者 in a question.
A choice can also sit inside a statement after 不知道 or 问, and it still takes 还是.
还是 also means "still" and "had better"; those are separate points.