Semi-major axis, vs aphelion, vs mean orbital distance?
I think your confusion is just an incorrect (though not uncommon!) visualization of a planetary orbit. The parent star (usually) doesn't lie at the center of the ellipse, but at one of the foci; only for circular orbits are the foci at the same location as the center of the ellipse. Therefore, for non-circular orbits, the aphelion distance is greater than the semi-major axis, and the average of the semi-major and semi-minor axes is the average distance to the center of the ellipse - not the star.

Mathematically, note that the perihelion and aphelion distances are related to the semi-major axis $a$ and eccentricity $e$ by
$$R_p=a(1-e),\quad R_a=a(1+e)$$
As a quick check, adding these together and dividing by 2 yields $a$. In the case of a circular orbit, where $e=0$, we have $R_p=R_a=a$.