Let me try to explain this.
A clause is a sentence which has a subject and a verb.
A phrase does not have a subject and verb.
Adverb - A word that modifies a verb is called an Adverb. e.g. He ran slowly. The adverb is slowly which modifies the verb ran.
Adverb Clause - A clause that modifies a verb. e.g. He ran when the dog chased. In this sentence ran is the verb of the main sentence. This verb is modified by the clause When the dog chased. As I said earlier a clause itself should contain a subject and verb. The Dog - Subject and Chased- Verb
Adverb Phrase - A phrase that modifies a verb. e.g. He kills dog for fun. In this sentence kills is the main verb and is modified by the phrase for fun.
I believe the same rules will apply to adjectives as well but with nouns.
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