What's the difference between semi-major axis and apoapsis? The semi-major axis is half of the diameter of the major axis of an ellipse by definition. So how does that make it any different from apoapsis, the furthest point an object is from a parent body in its orbit?

Both are radii along the longest axis, surely.
If the semi-major axis of an ellipse is a and the eccentricity is e,
then the distance from the center C to a focus F1 or F2 is c = ea.
Apoapsis is a + c and periapsis is a - c.

Ellipse with e &approx; 0.78:


For the Earth's orbit around the Sun, a = 149.6 million km and e = 0.0167, so


c = ea = 2.5 million km
aphelion = a + c = 152.1 million km
perihelion = a - c = 147.1 million km