If preserving the biodiversity of fish in the hobby is important to you, you should not cross breed any fish with distinctive genetic traits, especially if they come from different collection points. Whether or not the different fish have been scientifically described as separate species (which would make the crosses hybrids) is as immaterial as the whole wretched hybrid debate in the US.
As far as I know, two Tropheus variants have the term 'Kaiser' in their common name. Neither one seems to belong to the described species Tropheus moorii
, which makes calling them Kaisermoorii somewhat misleading. I believe it might be an outdated term. Futhermore, neither variant seems to belong to any described species. However, people appear to consider Kaiser as belonging to what's tentatively called sp. 'Ikola', while Kaiser II is believed to belong to sp. 'Black'. According to the Cichlid-forum.com profiles, the most appropriate names would be:
sp. "Ikola" (Ikola)
Kaiser II: Tropheus
sp. "Black" (Kiriza)
As Philippe pointed out, the main difference for the aquarist seems to be that Kaiser II have a narrower yellow band that extends into the dorsal fin, while in Kaiser the yellow band is wider, but the dorsal fin is mostly black.
Trivia: 'Kaiser' is the German word for emperor. (The term has its roots in Caesar
.) According to Wikipedia
, yellow was the color of Imperial China and is held as the symbolic color of the five legendary emperors of ancient China. In China, yellow often decorates royal palaces, altars and temples, and the color was used in the robes and attire of the emperors. I expect Kaiser Tropheus were named by a German Sinophile