usually they are designed to focus parallel radiation from an effectively infinitely distant source in outer space (with a parabolic shape). they can instead be designed to focus emission from a specific arbitrarily located relative fixed point at a specific arbitrary distance (with a spherical shape). the two curves are physically similar but focus differently.
i looked this up a little and it is not correct. spherical mirrors are used to approximate parts of parabolic mirrors. an ellipsoid mirror can focus between two focal points i think? then the receiver can be shaped curved to make the different “pixels” work out. there can be 1 or 2 or 3 mirrors …