the use of 9H and 10H only refers to the hardness of ceramic material when tested - they test a block of the material by scratching (Mohs hardness test)
The other marketing hype is the "9H or 10H" implying the coating is hard to scratch which is not true. 9H material is harder than quartz. I'll bet I can scratch any car with ceramic coating with some quartz crystals.
The 9H stuff with regards to ceramic coatings refers to a graphite/lead pencil hardness test - generally from 9B (soft) to 9H (hard). 9H indicates it cannot be scratched with a 9H lead pencil. Some coats go as far as claiming 10-14H hardness, which is dubious as this does not exist on the scale (though you could say "beyond 9H").
Further, the hardness of a ceramic coat depends on the hardness of the substrate underneath (ie., the paint/clear coat). So at best, ceramic coats
should claim to improve hardness by a few points on the lead pencil scale relative to uncoated paint (some decent brands like CarPro do this), rather than state absolute hardness claims.
The Mohs hardness scale is completely separate. Coated or not, you could scratch car paint with a copper coin (~3.5 on the Mohs scale - a fraction of properly hard materials).
Most ceramic coats leave a slick surface that prevents dirt and grime from sticking too much, making washing easier. Quality coats provide light scratch/swirl, water spotting, etching, etc protection at best. They all need maintenance and maybe a top-up, though nowhere near as often as a traditional wax.