Acetobacter and lactobacillus are prokaryotes, and Mucor and yeast are eukaryotes. This is the broadest classification.

It's hard to say the type of metabolism, because these names all represent a kind of organism, and there are many species in the following branches, and different species have different metabolic patterns. Generally speaking, most acetic acid bacteria belong to facultative anaerobic; Mucor belongs to aerobic; Lactic acid bacteria are facultative anaerobic or anaerobic, and yeast is facultative anaerobic. They are all heterotrophic microorganisms.