It depends on how you use them. 'Fast' can be either an adjective or an adverb. Remember that adverbs go with verbs (that's why the name is 'adverb' - literally 'next to/with a verb') while adjectives go with nouns. Look at these examples: a) 'I drive fast' - fast is an adverb (it describes the verb 'to drive' - how it is). b) 'The car is fast' - fast is an adjective (it describes the noun 'car' - what it is). So the comparative 'faster' can also be an adverb or adjective depending on how it's used: c) 'I drive faster than you do' - here, faster is a comparative adverb describing (and comparing) how two people drive d) 'The green car is faster than the red car' - here, faster is a comparative adjective describing (and comparing) a characteristic of two nouns.
