'Adverbial phrase (or adverb phrase) is the term for two or more words which play the role of an adverb ...'
An adverbial phrase and an adverb phrase are quite different. As I said before, adverbial is a function, and can be realised by several categories of phrase such as a PP ("He spoke with enthusiasm"), an AdvP ("He spoke quickly") and so on.
An adverb phrase, by contrast, is a phrase that has an adverb as head. Here are two adverb phrases:
1. "Quite separately from this issue". (the adverb "separately" is head)
2. "Happily for the boys". (the adverb "happily" is head)
It's extremely important for students to grasp this difference.