I think the search that you refer to is Grover's algorithm: https://en.wikipedia.org/wiki/Grover's_algorithm
Yes, Quantum computers have other known uses besides Shor's and Grover's algorithms. Specifically, they can simulate other quantum systems, and also do a few other things such as solving algorithms based on quantum walks. See https://en.wikipedia.org/wiki/Quantum_algorithm
I have a similar question to yours. Do the D-Wave people claim any mapping of their hardware to a known quantum algorithm such as those at the last link above, or what?