No verbs in phrases

I was consulting the Longman Dictionary of Language Teaching and Applied Linguistics for a clear definition of phrase. It refered me to clause, where I found the following definition: "A phrase is a group of words which form a grammatical unit." Fine, so far. "A phrase does not contain a finite verb." Oops!

I assume what the authors (Jack Richards, John Platt & Heidi Platt) are trying to do here is distinguish phrase from clause and to specify just what kind of grammatical unit we are talking about. But this limitation puts us in serious trouble, as the last part of the definition should make clear. "Phrases are usually classsified according to their central word or HEAD. e.g., NOUN PHRASE¹, VERB PHRASE, etc." (By the way, the note on noun phrase seems to be unresolved, as far as I can tell.)

So, verb phrases are types of phrases, but only when they do not include a finite verbs. But if we look up verb phrase, we find that it is a "part of a sentence that includes the main verb." Just be be absolutely sure we're not missing something, let's have a look at the example in which, we are told, everything except Tom is the verb phrase.

Tom gave a watch to his daughter.

Clearly, gave is a finite verb.

And we never did get to find out what kind of grammatical unit phrases are, did we? Sigh.