Mbuna, peacocks and haps are all Lake Malawi african cichlids (though there are different types of haps in Lake Victoria).
Mbuna's are largely herbivorous and have territorial and aggressive traits. Generally they're smaller than most peacocks and haps. In the wild they largely subside on algae-grazing. Their territoriality (in the wild) is used to protect and usurp their food source (algae covered rocks which are highly prized); these fish are rock dwellers, and mbuna means "rock" fish in one of the local languages where they originate from. With many (not all) mbuna species both genders are colorful. Most are in the 4"-6" size range, though some species max out at 3" and others at 8".
Peacocks and most haps are more predatory in nature and are geared more towards eating other fish, insects, aquatic crustaceans and mollusks and the like. They are more open water fish and less aggressive and territorial when compared to mbuna's. They're usually larger than mbuna's, with many peacocks being in the 5"-7" size range and haps being 7"+ (with some haps approaching and even exceeding a foot in length). With most peacock and hap species, the males are the ones with the vibrant colors.
In an aquarium setting, each of the above groupings are best kept with each other (though I suppose haps can coexist better with each other than either group can with mbuna's).
Example of a Mbuna:
A nearly 3" Pseudotropheus demasoni
Example of a Hap:
10" Dimiochromis compressiceps (Malawi Eye-Biter) (with smaller haps, cyrtocara moorii in proximity)