The farthest point needs its center
Aphelion measures separation from the Sun and apogee from Earth. A spacecraft’s solar aphelion is not necessarily the moment of greatest separation from Earth.
In an ideal ellipse, apoapsis lies at the far end of the major axis from the occupied focus, at a(1+e). Adding its distance to periapsis distance gives 2a.
Slower motion does not mean stopping
Equal areas in equal times imply slower motion near apoapsis than near periapsis. The object still moves around the orbit rather than stopping and reversing along the same path.
Earth-satellite reports commonly use apogee altitude above a reference surface, distinct from center-to-center distance. Those quantities require consistent conversion before orbital comparisons.
Changing the opposite end
A suitable prograde speed change at apoapsis can raise periapsis, while a reduction lowers it. The maneuver changes the orbit as a whole rather than independently shifting a drawing’s endpoint.
Open ideal parabolic or hyperbolic paths lack a finite apoapsis. The same two-apsis diagram cannot be applied indiscriminately, and actual changes depend on gravity, thrust direction and magnitude.