DAZ Studio comes with four different hairstyles for Genesis: Duke, SallyMae, Aldora, and WildMane. You can use them on any Genesis shape.
If you have non-Genesis hair (like the hair that comes with Girl 4 Base) and want to use it with Genesis, I have a tutorial that covers that process (along with other hair-related topics). It’s almost always possible, though sometimes it can take a bit of work. The link is in my signature below.
Note that if you buy both G4 Base and the G4 Shape for Genesis, you can use the G4 skin texture on Genesis.