What is the difference in part of speech, meaning, and usage between ‘만’, ‘뿐’, and ‘밖에’?
Both '만' and '뿐' mean 'only', but I'd have to say I hear '만' a lot more. '뿐' also sounds slightly more negative in some contexts.
밖에 actually means 'apart from' or 'outside' is generally used with the verb '없다'.
Let's look at some examples:
나는 파란색 만 있어. // I only have the blue one.
Notice the verb is '있다'.
나는 파란색 밖에 없어. // I don't have any apart from the blue one.
The verb used here is '없다'.
내 여름 휴가는 오직 1주일 뿐이야. / I only have a week of summer vacation.
Here you can clearly see the speaker is dissatisfied with the amount of weeks that they have for their vacation.