What is the difference between cytology and microbiology

Cytology almost invariably refers to the study of how cells work together in a multicellular organism, and how the behavior of those cells shape the anatomy and physiology of a multicellular organisms.

Microbiology refers exclusively to the study of organisms (single- and multicellular, and in the case of viruses, acellular) that are too small to see.

microbiology is the branch of biology that deals with microorganisms and their effects on other living organisms .
cytology is the branch of biology that deals with the formation, structure, and function of cells.

Cytology is the study of cells. Microbiology is the study of microorganisms; more specifically, the branch of biology that deals with microorganisms and their effects on other living organisms.