kcm is hwen he took the nine tails chakara, and used it during the beginning of the war, and also that was when he blocked A's attack. BM is what he turned in to when he was fighting obito, and he got that long coat of chakara.
bm naruto is the one with the long chakra cloak and has all those markings all over his body and can turn in to chakra based Kurama,
Km naruto is the previous form and is the one he acquired after "controlling" kurama.
KCM was before naruto and karama decided to work as a team. He was just utilizing some chakra he took from karama. BM is as close as we see naruto get to a host transformation so far. His seal is unlocked and him and karama work as one. There isn't exactly any chapter(s) in which everything is explained. you get the details as the story progresses. sorry you missed it.