The equivalent for periapsis of a body in Earth orbit is perigee, also called perigee height.
Unlike with all other bodies, mission planners are usually more interested in the height above the surface for low Earth orbit spacecraft. Hence perigee height refers to the distance between the body and the Earth's surface rather than the distance between the body and the Earth's centre of mass, for all objects in Earth orbit. This does not occur because the word perigee is special in some way, but rather because frequent inaccurate usage has effectively shortened perigee height to perigee and replaced the other meaning.
If you wish to anambiguously use the same measurements as with all other bodies, it is best to say perifocal distance rather than perigee.
The distance where a body's orbit is farthest from the Earth is known as apogee.
- J.R. Wertz - Orbits and astrodynamics in J.R. Wertz, D.F. Everett & J.J. Puschell eds. Space mission engineering: The new SMAD ISBN 978-1-881883-15-9 p. 202