a或者b
A or B - multiple possibilities
a還是b
is it A? or is it B?
“或” most corresponds to our "or", you will often see this single character in a sentence like
A (或:B)
in spoken language they say 或者 (huo2zhe3)
as i undersatnd it, if you use the meanings in the same sentence, the meanings change like this:
你想吃麵 或者 飯
you want to eat noodles or rice!
你想吃麵 還是 (想吃)飯
do you want to eat noodles? "or is it" (還是) rice (that you want).....
notice that chinese speakers don't add 嗎 in this style of question, because "還是" is a signal to the listener that you are unsure which is the case, implicitly asking the other party a question, so 嗎 becomes unnecessary. (The same is true for things like 什麼, I never hear: 你想要什麼嗎, only 你想要什麼?. )
(I hope if I am wrong, a native speaker will correct or clarify)