What's the difference between graphite, nanotubes, and fullerenes?
All three carbon modifications indeed contain covalently bond carbon atoms. The $sp^2$-hybridized C atoms are connected by $\sigma$ and delocalized $\pi$ bonds in all cases. It is the geometric arrangement of the atoms that differentiates the modifications: Stacked planes in graphite, fullerenes: ball-shaped molecules (hence the name buckyball), and for carbon nanotubes, the name is quite self-explanatory.

A single layer of the graphite structure:



A $\ce{C60}$ fullerene molecule:



And finally some carbon nanotubes: