I was wondering why R refers to the distribution family as an "error distribution" in the context of generalized linear models? Normally distributed errors(residuals) of a fitted model are a key assumption in simple linear regression. Yet it is my understanding that we switch to generalized linear models when this assumption cant be met because it allows the response variable (Y) to follow a non-normal distribution in the exponential family, which has nothing to do with any kind of "error distribution"?
Presumably this nomenclature is chosen simply to draw an analogy between the GLM and linear regression. You are correct that this term is not strictly accurate, since the family of distributions chosen for the GLM is not actually the distribution of an "error" quantity in the model. One can construct quantities in the GLM that are essentially measures of the "error" in each individual observation (the best being the underlying deviance errors for which the deviance residuals are an estimator). While the distribution of these "errors" is affected by specification of the family of distributions used in the GLM, they have their own distribution.