Adverbs are, of course adverbials, but not all adverbials are adverbs.
Match the term in italics to the definition.
He left when he saw me.
He left at six o'clock.
He left because he need to catch a train.
He left through that door.
He left sobbing loudly.
He left by bus.
He left last August.
He left earlier.
He left to get his train.
He left slowly.
adverb - manner
adverbial - non-finite (participial) clause
adverbial - time clause
adverbial - prepositional manner phrase
adverbial prepositional place phrase
adverbial - infinitive of purpose
adverbial - prepositional time phrase
adverbial - noun time phrase
adverb - time
adverbial clause - reason