Diamond is one form of carbon; the other is graphite. To distinguish them, we write:
Diamond: C(s,diamond)
Graphite: C(s,graphite)
The s stands for solid.
Both diamond and graphite are allotropes of carbon. There are other exotic allotropes of carbon (graphenes and fullerenes among them) but they are much less common.
A diamond consists of a giant three-dimensional network of carbon atoms.