It might be good to understand the difference between an adverb and an adverbial construction. Let's have a look at these phrases:

a) He runs fast.
b) It is a fast car.

In a) fast is an adverb and in b) it is an adjective. In a) it refers to the verb (and therefore has to be an adverb), in b) it refers to a noun (and therefore can only be an adjective).

a) He runs slowly.
b) It is a slow car.

Here we see the difference more clearly, -ly is the English ending for adverbs (even though not all adverbs do use this ending).

Example       He does it well. He does it with great care.     She works smilingly. She works with a smile.     We talk pleasantly. We talk with pleasure.

Well, smilingly and pleasantly are adverbs, with great care, with a smile and with pleasure are adverbial constructions that havethe function of an adverb in these sentences, but can have other functions, too.