botany vs mycology

botany and mycology both are nouns.

Word	Noun	Adjective	Verb	Adverb
botany	Yes	No	No	No
mycology	Yes	No	No	No

As nouns, mycology is a hyponym of botany; that is, mycology is a word with a more specific, narrower meaning than botany:

botany: the branch of biology that studies plants
mycology: the branch of botany that studies fungi and fungus-caused diseases

Other hyponyms of botany include pomology, palaeobotany, paleobotany, algology, phycology, pteridology.

botany (noun)	mycology (noun)
the branch of biology that studies plants	the branch of botany that studies fungi and fungus-caused diseases
all the plant life in a particular region or period