If you are the DM, you can make the perform skill as specific or as broad as you want it to be.
For example, if you think just having perform (guitar) is too broad a skill, make the bard take a specific style of music to be played on the instrument. perform (jazz guitar), perform (rock guitar), perform (bluegrass guitar), etc.
Of course, this won't work with all instruments. Bagpipes and spoons sound the same, no matter what type of song you're playing with them.
With singing, it's more the type of song being sung than it is the style of singing. There are ballads, story songs, anthems, epics, lyrical, melodies, chants. This is what I interprete the Player's Handbook referring to for the choices under perform. The style you sing each type of song is sort of the bard's trademark, or signature. Everything song Frank Sinatra sang had his trademark style. This is done through the arrangement.
A ballad can be performed by a single person; two or more harmonizing; in a country style; in an operatic style; in a rock style; in a jazz style; in an R&B style; in a gospel style; in a rap style; in a barbershop style; in a Mongolian throat-singing style. All the same song, just sung in a different style. And even those styles have subcategories. East Coast rap, West Coast rap, gangsta rap, rock-rap. Southern Gospel. Contemporary Gospel. Traditional Gospel. Speed Metal Gospel. Just check out a full list of the Grammy Nominations sometime for all of the different styles of music, and remember -- any one song can be performed using any of those various styles.