I think not; rather, I think it could refer to either of those things. The tag wiki says:
This tag is for questions seeking a phrase that fits a meaning. If you are looking for a word, or don't care, see the "word-request" tag too.
The idea, then: if you have a concept or idea, and want to know how to express it in English, you either want a single-word response or one longer than that. If you want a single word, use word-request. If you want something longer, use phrase-request.
As a side note, I'm not sure I agree with the tag wiki when it says we ought to be double-tagging questions with both word-request and phrase-request. But I suppose that's another meta discussion!
(Also I believe your definition #1 is specifically referred to as a noun phrase. I think in practice, if a user requests a word and only a noun phrase is available, they weren't going to know that from the start, so they lack this knowledge to decide which tag to use. Either way I don't think it's a big deal; if you request a word and only a phrase exists, someone will tell you, and vice versa. :) )