Hollow ground blades have a secondary straight bevel for the actual cutting edge, the hollow is a primary grind that goes either part-way or all the way to the spine and is intended to help lower friction against things like food. It creates an air pocket preventing suction to the surface.

Convex is just done with some sort of slack-belt sharpener usually. It can either be the edge grind, or convex can have a secondary edge bevel as well.

Most of the guided sharpeners are best used for the small secondary bevel cutting edges anyways.

If you get good with the stones, consider upgrading to the larger Japanese style wet-stones.