Definition

Kinases refer to enzymes that catalyze the transfer of a phosphate group from ATP or GTP to its protein substrates

Phosphorylases refer to enzymes which catalyze phosphorylation through inorganic phosphates

Addition of phosphate groups 

Kinases add phosphate groups to existing organic molecules (does not break the bonds in the substrate)

Addition of phosphate groups by phosphorylases break bonds in the substrate 

Regulation

Regulated by phosphorylation

Regulated by phosphorylation or allosteric regulation

Co-substrate requirement

Uses a phosphate group from ATP or GTP  for phosphorylation reactions

Uses inorganic phosphate groups as the donor of phosphate groups for the formation of a phosphorylated intermediate 

Substrate specificity

Kinases typically phosphorylates specific target molecules (e.g. proteins, lipids, carbohydrates)

Phosphorylases specifically phosphorylate glycogen or other similar polysaccharides 

Functions

Kinases play a vital role in cellular signaling, metabolism, cell division and gene expression  

Phosphorylases are involved in regulation of energy metabolism (specifically glycogen breakdown)