As @tel said, there is no clear difference available since there is no international authority which manages such things (like IUPAC) when it comes to biological terms. However, these terms can be understood and differentiated a bit more easily, as long as you don't get into deeper details.
Posphotransferase is a kind of transferase that transfers a phosphate group from one compound to another. The type of substrate remains unspecified (dictionary.com).
Kinase is a type of phosphotransferase that transfers a phosphate group from high-energy phosphate donating molecules (usually ATP) to anothrr molecule. Here, one substrate is specified (Wikipedia).
Phosphorylase is an enzyme that adds an inorganic phosphate ($\ce{PO_4^{3-}}$) to a substrate molecule. The inorganic substrate is not transferred, it is directly added to a molecule (Wikipedia).
Hydrolase is an enzyme that hydrolyzes a substrate i.e. breaks a covalent bond in a molecule and adds water to the resulting molecules. Its like $$\ce{A-B + H_2O \rightarrow A-OH + B-H}$$ where A-B is a single substrate molecule (Wikipedia).
Phosphatase is a type of hydrolase that hydrolyzes the bond between a molecule and phosphate group, resulting in the formation of inorganic phosphate and an alcohol. It is like $$\ce{A-PO_4^{2-} + H_2O \rightarrow A-OH + HPO_4^{2-}}$$ where A becomes an alcohol (Wikipedia).
PS: I am not saying that these are the universally accepted definitions of the corresponding enzymes. These are just examples to help you better understand the meaning of these terms. However, you can always find exceptions to these definitions.