There are two general distinctions of giant robot shows (based on classifications in the Super Robot Wars games), Real and Super. Exactly what defines which is a matter of much debate on /m/, but in general it has less to do with the robots themselves than how they're presented to the audience.
In super robot shows, the robot is a heroic presence. Often one of a kind, it is almost as much of a character as its pilot. They tend to bend the laws of physics as far as they'll go and sometimes replace them wholesale (Gunbuster wrote its own physics textbook when the real one proved to be a problem). Getter Robo is the prototypical Super Robot show.
In real robot shows, the robot is far more of a tool to be used. Often mass produced, they're very much just weapons. The "real" classification doesn't mean they don't bend physics to the breaking point, it's just that they do try to be a bit more realistic about things. Macross is very much the prototypical real robot show. Gundam is often seen as the "first" real, but it holds on to a lot of super characteristics and tends to be more of a bridge between the two.