Are adverb phrases and adverbial phrases two different grammatical terms? If so, what is the difference between the two?

One of my friends said that the two are different and also gave explanations as given below.
Adverb phrases are phrases that has an adverb in it. For example, "frequently visiting the doctor" is a phrase in which an adverb "frequently" is seen.
Adverbial phrases are phrases that acts as an adverb in a sentence. For example, "Bacteria grow at the edge of a pond" is a sentence in which "at the edge of a pond" is a phrase acting as an adverb.

Is this right? Can anyone help me understand this?
Those mean the same thing. The only difference is how they are named.
thanks for the answer