Three kinds of pseudomorph exist:
A paramorph (also called allomorph) is a mineral changed on the molecular level only. It has the same chemical composition, but with a different structure. The mineral looks identical to the original unaltered form. This occurs, as an example, in the Aragonite to Calcite change.
An infiltration pseudomorph is a pseudomorph in which one mineral is replaced by another. The appearance of the mineral remains unchanged.
An incrustation pseudomorph results from a process by which a mineral is coated by another and the encased mineral dissolves. The encasing mineral remains intact, hence hollow. Or another mineral filling the space of previously dissolved matter.
Pseudomorphs are also common in Paleontology. Fossils are often formed by pseudomorphic replacement of the remains by mineral matter. Examples would include Petrified wood and pyritized gastropod shells.