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What's the difference between a verb phrase and a predicate?
GB
Comments 
All predicates are a verb phrase, but the reverse is not true.
In the wider definition, there is no difference; they are the same. In a narrower definition also used, a verb phrase is only part of the predicate-- it includes only the direct verbal forms (auxiliaries, participles, etc):

I have been skiing all day.

I -- Subject
have been skiing all day -- Predicate (and Verb Phrase in the wider sense)
have been skiiing -- Verb Phrase (in the narrower sense)
all day -- Adverbial
Students: We have free audio pronunciation exercises.
Alright... that is fine.
Thanx
GB
These two terms fall into two different categories: predicate is a part of sentence and verb or verb phrase is a part of speech.

Ania Kieturakis