I've looked in several sources, but I'm still confused. This is what I have so far:

• A phosphotransferase catalyzes the addition of a phosphate group.

• A kinase is a type of phosphotransferase that transfers a phosphate group from ATP to a substrate.

• A phosphorylase is a type of phosphotransferase that catalyzes the addition of a phosphate group from an inorganic phosphate (HPO4) to a substrate.

• A hydrolase catalyzes the hydrolysis of a chemical bond.

• A phosphatase is a type of hydrolase that removes a phosphate group.

Is this right?

EDIT: Also adding to the confusion is the enzyme Phosphorylase kinase, which is the kinase that phosphorylates the enzyme Glycogen phosphorylase, which hydrolyzes glycogen.