This is rather like saying "what's the difference between a carnivore and a mammal". "Carnivore" is a way of describing animals (etc) according to what they do (their function) "Mammal" is a class of animals. Some mammals are always carnivores, some mammals are sometimes carnivores, and there are carnivores that aren't mammals.

We can classify words into "parts of speech", such as nouns, verbs, etc. One of these parts of speech is the adverb. These differ mainly from adjectives in that adverbs attach to verbs and other parts of speech, but not to nouns. Of the various parts of speech, adverbs are perhaps the most varied, with lots of special cases. It is a bit of a dumping category for lots of words that aren't anything else.

A typical function for an adverb is to modify a verb: "He ran quickly" or to modify an adjective "He is very big" or add supplementary information to a sentence "Unfortunately, he missed the haystack".

In these roles they are adjuncts. They could be removed from the sentence without affecting the overall structure. They might carry important information, but they aren't required by the grammar.

But there are other adjuncts. Adjectives can be adjuncts: "He is a big man" And not only words, phrases can also be adjuncts "Passing the salt, Mary whispered a secret." or "People that play tennis sometimes get injured." Strictly "adjunct" is a role of a phrase not of a word, but some phrases have only one word.

There is a colossal range of adjuncts. They are distinct from other functional elements such as "subjects" or "complements" because if you omit a complement the sentence either becomes ungrammatical, or the grammar changes.

For example "back" is an adverb in the sentence "She put the cheese back." But it is not an adjunct. It is required and cannot be omitted. "*She put the cheese" is ungrammatical.

So, adverbs are a type of word. Adjunct is a function that a phrase can have. Adverbs can often head a phrase that is an adjunct. But not every use of an adverb is as an adjunct, and there are very many adjunct phrases that are not headed by an adverb.

This is rather like saying "what's the difference between a carnivore and a mammal". "Carnivore" is a way of describing animals (etc) according to what they do (their function) "Mammal" is a class of animals. Some mammals are always carnivores, some mammals are sometimes carnivores, and there are carnivores that aren't mammals.

We can classify words into "parts of speech", such as nouns, verbs, etc. One of these parts of speech is the adverb. These differ mainly from adjectives in that adverbs attach to verbs and other parts of speech, but not to nouns. Of the various parts of speech, adverbs are perhaps the most varied, with lots of special cases. It is a bit of a dumping category for lots of words that aren't anything else.

A typical function for an adverb is to modify a verb: "He ran quickly" or to modify an adjective "He is very big" or add supplementary information to a sentence "Unfortunately, he missed the haystack".

In these roles they are adjuncts. They could be removed from the sentence without affecting the overall structure. They might carry important information, but they aren't required by the grammar.

But there are other adjuncts, and not only words, phrases can also be adjuncts "Passing the salt, Mary whispered a secret." or "People that play tennis sometimes get injured." Strictly "adjunct" is a role of a phrase in the structure of a clause, not of a word in the structure of a phrase, but some phrases have only one word.

There is a colossal range of adjuncts. They are distinct from other functional elements such as "subjects" or "complements" because if you omit a complement the sentence either becomes ungrammatical, or the grammar changes.

For example "back" is an adverb in the sentence "She put the cheese back." But it is not an adjunct. It is required and cannot be omitted. "*She put the cheese" is ungrammatical.

So, adverbs are a type of word. Adjunct is a function that a phrase can have. Adverbs can often head a phrase that is an adjunct. But not every use of an adverb is as an adjunct, and there are very many adjunct phrases that are not headed by an adverb.