The Moon does, in fact, appear about 30% larger in area at perigee, the point in its elliptical orbit when it’s closest to the Earth, compared with apogee, the point is elliptical orbit when it’s farthest from the Earth. A super moon is a full moon at perigee.
You’re right that the moon presents the same area whether it’s near the horizon or directly overhead. That apparent difference is indeed your eyes playing tricks on you. It seems smaller when it’s overhead in the open sky and there are no nearby trees, houses, etc. for reference.
#moonchain