The term 'gravity wave' is a bit ambiguous since it generally refers to things (such as certain cloud formations) that have nothing to do with gravity in the astronomical sense. Gravitational radiation and gravitational waves are the generally preferred terms. But if the proper context is available such terminology squabbles are just that.
Yes DRP assumes that gravitational waves, if they actually exist, will propagate at the speed of light.
Note that gravitational waves have no direct relationship with gravitational force. Specifically, gravitational waves are not the same as changes in gravitational force. We can already measure the latter.
Gravitational radiation is believed by most theories to propagate through "empty" space as a transverse wave, just like electromagnetic radiation. In both cases the physical medium being "waved" is of course hotly contested and very theory dependent. Is it a variable density aether? The space-time continuum? Dark matter and dark energy? Or maybe its something we haven't thought of yet. In any case the math generated by the theory is/must-be the same/equivalent or the theory is automatically falsified.
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Transverse means the forces involved oscillate back and forth sideways to the direction of propagation of the wave front.
Longitudinal waves have forces that oscillate forward and backward in the direction of wave front propagation.
Both of these are a type of bulk wave, waves that travel within the bulk region of a medium, well away from (greater than a wave length or two) any boundaries.
Longitudinal waves can travel within any medium. Transverse waves can only travel within a solid. Or a medium that is able to behave like a solid in at least some ways.
The only other type of wave know is a surface wave. As you might guess from the above discussion, they travel at or very close to the boundary of the medium they are in. They behave like a combination of longitudinal and transverse waves. Ocean waves are an example of surface waves that almost all of us have seen.
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Gravitational force is believed (assumed/guessed/postulated) by DRP to propagate as an omnidirectional particle flow - IOW, not a wave. As a consequence the forces involved always point in one direction - toward the center of the nearest mass. If the nearest mass is far enough away and moving fast enough, the pointed direction can lag the exact center due to propagation delay (aberration).
Other theories either make no guess (eg Newton) as to a physical mechanism or assume / guess / postulate some other physical mechanism (eg GR).
Another difference - gravitational waves (according to GR) are generated when a mass is accelerated but that same mass' gravitational force (according to GR and any other theory that matches observation) is always on. This is similar to the behavior of electrons. An electron's electric field is always on, but when it moves there is also a magnetic field and when it is accelerated there is also an electromagnetic field.
As the article you link states, the <u>confirmed</u> discovery of gravitational waves will be a big deal. I imagine it will make the nightly news if it happens.
