Crystal face refers to when a crystal has a smooth plane formed on its surface. Certain crystal processes such as twinning usually occur on the crystal face. Cleavage plane, on the other hand, refers to the property of crystals, which allows them to divide into certain structural planes. Crystal faces usually reflect the internal structures of minerals through their outward planar surfaces.
They are mostly discussed in relation to terms like Crystallographic Axes, Crystal symmetry, etc. Crystal faces are usually indicated using different kinds of numbers. These numbers are used mostly to describe the halo ray path through crystals. In contrast, the bonds between atoms or molecules are made less strong due to the cleavage plane, and this usually causes the surface of a mineral to look shiny and smooth.
Usually, cleavage planes are used to identify minerals. Unlike in crystal face where atoms bond with one another, cleavage planes are usually parallel to crystal faces.