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