Comparing diamond and graphite, for example: Both have covalent bonding-- electrons shared between the carbon atoms. In diamond, each carbon atom is the same distance to each of its neighboring carbon atoms in a rigid network... like a playstructure on a playground. In graphite, carbon atoms are attached by strong covalent bonds also, but in stacked up layers with weaker forces between the layers... like a stack of pancakes stuck together by syrup. So when you draw with a graphite pencil, layers of the carbon are being scraped off onto your paper.
Recently, new carbon structures have been discovered. In the shape of icosohedrons (20 sided round shapes) named Fullerenes (after Buckminster-Fuller). 60 carbon atoms are covalently bonded together to form a hollow sphere.....different shapes can be constructed, as if the graphite layers were rolled up to form pipes....