Basically, a sub-genre contains elements of another genre, but can't be called that genre. It however, isn't a genre in its own right.
b)Nay, it is but a subgenre
b)Read this! *directs to this article*
grunge -- commonly used to describe a type of rock that's somewhat on the heavy side. throaty voices and guitars with heavy gain and bass are common.
metal -- the heaviest form of rock. the music is sometimes classified as angry, often with screaming or growling voices incorporated, as well as drums with double bass, heavy guitar progressions in a minor key, high gain lead guitar solos, and a fast tempo. metal even has its own subgenres, such as death metal (commonly the music associated with the style generalization of "goths"), hair metal, melodic metal, etc.
punk -- debatably the fastest paced form of rock. often the music is simple, consisting of power chords and simple lead guitar parts very frequently in a major key, and simple but fast paced drumbeats with a fill added every so often. punk is sometimes otherwise defined by politically critical lyrics. this is one of the genres used also to classify a certain group of people, who are often automatically judged as immature, skaters, stoners, and pricks.
hardcore -- music that is similar to metal in its heavy components (such as incorporated screaming vocals, drums with double bass, etc.) but with thinner singing voices, a higher pitched and thinner scream, and a rhythm guitar distortion with less gain and bass and more treble. also a term misused to generalize people as tough or fearless, and usually a style with a lot of body piercings is included in this generalization.
indie -- rock music that is simply classified as different from the mainstream. this genre is often misused and originally spawned to describe bands or artists that are unsigned by a record label (hence "indie" as short for "independent"), yet a genre is not supposed to define a band's business state but the style of their music. this genre is most commonly used as a term to generalize people in the UK, basically to describe people who reject anything mainstream and conform to being unique. the term "scene" is used for this purpose in america.
emo -- a softer form of rock with thin, crisp guitar distortion. the music often takes influence from punk, hardcore, and indie music, but the vocals are sung often in a higher end vocal range with a thin, untrained voice. the term is often misused to describe music with depressing lyrics, although the purpose of a genre does not include generalizing the lyrics, simply the music. this subgenre is probably the most commonly used to classify people, given with a negative connotation and usually rejected or denied by the recipient. this subgenre is used to describe people depressed over petty matters, and is also commonly associated with a style which includes males with long bangs covering one eye and girls' jeans. the term "scene" may also describe this style.
screamo -- music in between hardcore and emo. bands which fall under this subgenre are commonly mistaken to define emo.