Here's my understanding:
- A contractor saw has a motor hanging out the back and runs on 110V
- A cabinet saw has the motor inside a cabinet and runs on 220V
- A hybrid saw has the motor inside a cabinet and runs on 110V
Of course, this is a gross simplification, but that's where the hybridity comes from (yes folks, hybridity is a real word

): Form factor and voltage.
Some hybrid saws have the trunnions mounted to the cabinet (like a cabinet saw), others have them mounted to the table (like a contractor saw). Also, I've rewired my hybrid saw to 220V, but that doesn't make it a cabinet saw (HP is the real differentiator - with 110V you can't get above 2HP on a 20A circuit).
In general, hybrids are more stable/ solid than contractor saws, and the enclosed cabinet provides better dust collection.
In general, contractor saws are meant to be portable. But there are lots of examples that make these statements guidelines, not rules.