Body-specific names
A solar periapsis is perihelion and an Earth-centered one perigee. Other body-specific names express the same closest-approach concept.
The center matters: Mars at perihelion is not necessarily closest to Earth. Minimum separation between moving planets requires comparing their positions at corresponding times.
Focal distance and surface altitude
For an ideal ellipse, the central body occupies a focus and periapsis is the nearest end, at distance a(1−e).
Satellite reports often give perigee altitude, whereas orbital distances are measured from the center. Conversion needs an appropriate planetary radius or shape model; hundreds of kilometres above the ground is not that same distance from Earth’s center.
Motion and maneuvers at periapsis
Motion is faster near periapsis in an ideal Kepler ellipse. A suitable small prograde burn there raises the opposite apsis, while a retrograde change can lower it.
NASA also describes atmospheric drag near periapsis as a means of removing orbital energy. Actual maneuvers require direction, magnitude and environmental constraints; the location of a burn alone does not specify its outcome.