The point at which a general orbit is closest to the center of mass is known as its perifocus. Perifocal distance or periapsis are the names given to the distance between the perifocus and the center of mass.
The point at which a general orbit is farthest from the center of mass is known as apofocus. Celestial bodies have specific terms relating to the apsides of their orbits. Of particular importance is the fact that perigee is measured differently from the others.