Are bitters and ales all types of beers, is beer the general name for this group?

Beer is the overall title. That depending on what style guide you go off of can be divided down into two or three groups, generally though its divided into ale or lager depending on what type of yeast is used during fermentation. These groups are farther divided into subgroups(sour ales, bitters, stout, etc) and from there divided even further down into categories(I.e. bitter, special bitter, etc).