To put it simply, kinetic abilities explicitly involve moving a certain object. Hydrokinesis, in this example, involves explicitly moving or controlling the flow of water.
Manipulations, on the other hand, are a catch-all term for any power which falls under it's category. Hydrokinesis is, then, an aspect of water manipulation. But so are things such as Ice manipulation, water summoning, and a variety of other powers which have nothing to do with hydrokinesis, but do in general involve water