One similarity between a phrase and a clause is that the both of them can be a part of a sentence. However, the clause is more complicated.
Now, on the one hand, a phrase is an incomplete sentence, or we could say, "it is a part of a clause", and on the other hand, a clause can be an incomplete sentence as well, or can still stand on its own as a complete sentence.
Phrase:
A phrase (like I mentioned in the previous chapter) is a group of two or more words. This group of words acts as a single unit. That's, it expresses a single idea. One thing is sure, it does not form a complete sentence. The simple reason is because it lacks a subject-verb pair (sometimes it contains a subject without a verb, other times, a verb without a subject).