Lateral faults are not one of the three principal types of faults. A fault is a geologic structure produced as a result of brittle deformation of a rock. It results in blocks of rocks moving relatively one another.
There are three types of faults in a rock:
Normal fault
Thrust fault
Strike slip fault
Normal and reverse faults can also be referred to as dip-slip fault.
In a strike slip fault, two rocks slide past one another.
This is different from dip slip faults in which a block slides down or up of another.