haps = haplochromis - there are three main groups of malawis, these are typically the biggest.
Mbuna means rockdweller (another one of the groups) and that includes electric yellows, all the zebras, melanochromis and anything else with that general shape.
Peaocks are the other group, all of them come from the aulonocara genus, also called peacocks.
tang is short for tanganyika (spelling?) for example tropheus come from there, all the lamprologus, frontosa etc. You can keep them with malawis but not many people do.
HTH