What is the difference in sociology and social psychology or quantitative psychology?

The difference between these three fields can be and, in the case of two of them (sociology and social psychology), is a matter of perspective. Also, sociology also has a subfield call social psychology.

The perspective of sociology is that it is the study of the effects of society upon an organism and the development of societies.

Social psychology, in psychology, studies the effect of a society upon an organism and the effects that individuals can have on society. It will focus more on how organisms develop within a society.

I use the term organisms because some researchers in all these fields may study animal or insect societies, or even bacteria. Certain principles and mechanisms found in one society have be found to apply to other societies.

Quantitative psychology seeks to measure and define the mathematical relationships between factors, whether it is individual behavior or societal behavior, as a means of predicting outcomes when certain variables are present. They try to determine essential variables that influence a behavior or event and the relationshipss between those variables and outcomes.