Gorilla glue is strong, waterproof and it sands.
It behaves like a white glue, except that it foams (very slightly). It comes in dispenser bottles very similar to white glue. The big bottles are much better value. Difference in use to white glue is that you must wet the gluing surfaces before applying glue. The glue then reacts with the moisture to foam slightly. The glue will not grab for a few minutes, so that you can reposition parts if needed. You must not leave the glue exposed to air in its bottle otherwise the surface of the glue will go hard. Workable in 4 hours, fully set in 24.
An impact/contact adhesive is spread on both surfaces, is given a few minutes to semi cure. The two surfaces are then pushed together. The glue grabs instantly and you cannot reposition (with the exception of Timebond). It is more suited to gluing flat surfaces and veneering. With TimeBond you can repostion the pieces by sliding one over the other, but you only have about a minute. With impact glue putting pressure on the joint finishes the glue. It is very fast setting, almost instant. Contact/impact adhesives don't seem to sand very well.