Let us evaluate each statement:

1. Only graphite is soft and slippery, making it useful as a dry lubricant for machines running at high temperatures. Diamond is extremely hard and is used as an abrasive.
2. Diamond has a rigid three-dimensional tetrahedral network, whereas graphite has a two-dimensional planar layered structure.
3. Both diamond and graphite are giant covalent network solids formed entirely of carbon atoms; neither of them is ionic.
4. In diamond, each carbon atom undergoes $sp^3$ hybridisation and is covalently bonded to four other carbon atoms. In graphite, each carbon atom undergoes $sp^2$ hybridisation and is bonded to three other carbon atoms in the same plane. Therefore, this statement is the only correct one.