In water, surface waves operate principally under the effects of surface tension (small waves such as you'd find in a ripple tank, to about 0.1s period), or gravity, where the mass and inertia of the water moving up and down dominante.
There are also pressure waves, which are the result of compression and expansion of a medium. Water compresses poorly, whilst air compresses quite well and elastically. Sound is largely a phenomenon of pressure waves.
With the development of very sensitive instruments, gravitational waves in which the geometryof space-time itself is altered can now be detected. Despite the similarity in terms, "gravity waves" and "gravitational waves" are very different phenomena, and we'd need events at the scale of neutron star collisions to be ablet to create readily-detectable gravitational waves. Tonga Hunga was somewhat below this threshold.
There are also electromagnetic waves, experienced as EMR (including visible light), AC electric power transmission, and magnetic waves. Again, different phenomena, though the same underlying wave equations describe this behaviour.