Axial expansion
An axial seal moves across the face of a groove toward a parallel mating surface. It is often considered for door and hatch perimeters where the gap is normal to the mounting plane.
Radial-outward expansion
A radial-outward profile grows toward a surrounding bore or outside surface. It can be useful when the seal is mounted on an inner member and must contact an outer housing.
Radial-inward expansion
A radial-inward profile closes toward a shaft, drum, liner or container. It is frequently reviewed for annular interfaces and product-transfer equipment.
Make the choice from the section drawing
Names are less useful than geometry. Mark the fixed surface, moving surface, working gap and required contact direction on one cross-section. That drawing quickly identifies the appropriate expansion concept.