Similar names, entirely different things. Gravitational waves are the things generated by collapsing black holes and pairs of rotating neutron stars.
Gravity waves are what we're talking about here - so named because gravity is the controlling force behind the phenomenon. Mountain waves are probably a more commonly known example.
A parcel of air is pushed up by something like a thunderstorm or mountain and because it has higher density to the surrounding air, gravity causes it to return from whence it came. But it now has momentum so the parcel overshoots downwards until buoyancy overcomes it, pushing the parcel up. Again momentum causes overshoot and this cycle repeats setting up a wave.
tartare is correct.