Unlike with all other bodies, mission planners are usually more interested in the height above the surface for low Earth orbit spacecraft. Hence apogee 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 apogee is special in some way, but rather because frequent inaccurate usage has effectively shortened apogee height to apogee and replaced the other meaning.
If you wish to anambiguously use the same measurements as with all other bodies, it is best to say apofocus distance rather than apogee.
The point at which a body's orbit passes closest to the Earth is known as Perigee.
- 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