Simply speaking: both have "double bonds", in the sense that benzene has "alternating single & double bonds".
The double bonds are delocalized throughout the fused ring system(s), yielding "partial double bond".
N.B. For graphite, refer to "graphene".
I don't totally agree with Ka Ho's answer
Fullerene part is OK
but for graphite I think double bonds DO EXIST,
just that they are "moving" around very quickly, like that in benzene
making it "delocalized"