Generalized linear model, as its name suggests, is a generalization of general linear model or GLM. Some sources specify its acronym as GLZ to differentiate it from GLM while other sources still indicate it as GLM. The general linear model follows the normal distribution while the generalized linear model allows variables outside the normal distribution; hence, it is an extension.
For instance, GLZ is used when a researcher wants to identify the variables which are influencing consumers to buy certain products with the response variable as buying or not buying.