An adjectival clause is one which performs the function of an adjective.
The old man fell down. (adjective)
The man, who was very old, fell down. (adjectival clause)
The man with a sad face entered the room. (adjectival clause)
The man, with a sad face, entered the room. (adverbial clause)
An adverbial clause is one which performs the function of an adverb.
The boat rocked dangerously. (adverb)
The boat rocked when the sea was rough. (adverbial clause)
While the usage is established, I would not call them adverbial or adjectival clauses, in that they function differently from adverbs and adjectives in general. They tend to come after the noun they qualify. They also do not act like adverbs and adjectives. (No comparative or superlative forms. etc.) I would go with Huddleston & Pullum's (Cambridge Grammar of the English Language) terminology and just call them complements and adjuncts,