Aren't they the same thing?

A geodesic dome is a part of a buckyball, or, some other polyhedron.

The term geodesic commonly refers to a triangulated sphere, but, they can be made of trapezia, pentagons, triangulated pentagons, or, any of a number of other configurations. The reason the triangle is used for structures, is, it is the only rigid plane figure.

A buckyball is a structure that represents the C60-buckminsterfullerine molecule (http://www.3dchem.com/moremolecules.asp?ID=217&othername=Buckminsterfullerene). It has nothing to do with a geodesic dome.