Different theories "see" (interpret) gravity differently:
Netwon: an instantaneous force , three dimensions of space, space and time is fixed
Einstein: curvature of space time, not a force, wave field like theory,continuous smooth, cosmic sizes, four dimensions of spacetime with variable space and time
Quantum theory: gravitons are the carrier of gravity, discrete picture, atomic realm
Trying to precisely compare all these is difficult: The first two are quite complementary and Einsteins picture simplifies to Newtons in many cases; Nobody knows how to "unify" the last two..it's been one of the major objectives since the 1920's. Einstein shows that gravity occurs due to mass, energy and pressure.
String theory has a slightly different view from any of the above: It views all particles, gravitons included, as vibrating bits of two dimensional energy...different vibrational patterns cause different particles in 11 dimensional spacetime.
Gravity is also related to the other three forces (strong,weak, electromagnetic) but nobody knows exactly how. And Maybe Higgs bosons (field) are also related to gravity since they theoretically cause mass and mass in turn causes gravity.
In some vague sense you might consider curvature of space and aether "similar" in that both are "something". But curvature of spacetime is far more fundamental and subtle than "aether". Aether was postulated to carry light; it had nothing to do with any other force, such as gravity. gravitational curvature is unnecessary for the other forces; aether has been pretty well proven to be no existent.
"We know a lot, we understand little."