I am not sure if I got you right, but I think there are kind of two types, often combined:
Speed/Tempo and Style.
NETWORK MUSIC for example would just label the number and then the pace of the overal album, e.g. "18 - MEDIUM TEMPO" with a bit of a classification. See here for example. (https://productionmusic.fandom.com/wiki/List_of_Network_Music_albums)
(https://static.wikia.nocookie.net/productionmusic/images/4/4c/NM-018-originalCDcover.jpg)
(Image source: Production music Fandom)
OMNIMUSIC has a bunch of "genres" going on, but not in the conventioinal matter. You can have a "Synthpop" industrial song, but it also could be full of brass fanfares. The generic sleeve of an OMNIMUSIC CD usually uses only the "genres" and styles used on that album.
All of the "genres" at once [interestingly, they left out the top left tile which usually would show a violin for classical music..](Explanation here. (https://productionmusic.fandom.com/wiki/List_of_Omnimusic_CD/digital_albums))
(https://i.postimg.cc/WbhksqmH/OMI-OMN-0033.jpg)
If they used only certain type(s), the CD cover would actually show that, so you kind of knew what you can expect - in this case, a poutpourri of different themes.
(https://i.discogs.com/1xkgv-Kg07OCF8NCVII7oDRo33kmDHwdYkino4zC3rI/rs:fit/g:sm/q:90/h:600/w:600/czM6Ly9kaXNjb2dz/LWRhdGFiYXNlLWlt/YWdlcy9SLTY2MDMx/MDUtMTQyMjg5ODkw/My04NTM5LmpwZWc.jpeg)
(Image source: Discogs)
Or this album: The name "LIVING IN THE FUTURE" is already a good hint, but when you look at the genres: Industry, Future, Technology, Space - that should be helpful to identify the "genres" to expect:
(https://i.discogs.com/9PjVG2p1WQDkp0R4l2U1ORDmuJco-kFzcPtZQ88p4Kk/rs:fit/g:sm/q:90/h:600/w:596/czM6Ly9kaXNjb2dz/LWRhdGFiYXNlLWlt/YWdlcy9SLTY2NDYz/NzAtMTQyODYxMDMx/OS0yMDEyLmpwZWc.jpeg)
(Image source: Discogs)
What to expect from an album called SWEAT? Yes: Exactly that. Sports and "Power"! :D
(https://i.discogs.com/6qYMJDdyku3a8dO5MVlnxDQrMuOmjFR2Bg9vYPUYe3M/rs:fit/g:sm/q:90/h:600/w:600/czM6Ly9kaXNjb2dz/LWRhdGFiYXNlLWlt/YWdlcy9SLTU3NjA0/MTktMTQwMTg5OTE5/MS03Njc2LmpwZWc.jpeg)
(Image source: Discogs)
I know this is not quite "genre" as said above, but I think it kind of classifies. If you are looking for natural themes or sports, you will have fast drums, brass and horns. Then you would probably check the sleeve or catalogue.
MUSIC HOUSE would also have some basic categorizations.
Many labels appeared to have sub-labels or whole new "collections" going on (e.g. NETWORK MUSIC has BRAINSTORM for really fast, 90s pop/rock themes or MATCH MUSIC XS for Club/Eurodance music)