Sansui did this a lot in the late 70's and early 80's, they'd take an existing model and rebadge it as a "classique" with an updated model number. This appears to have been part of a program where they marketed units together in a package deal at a special price for selected retailers. Usually this stuff was found in department stores or other mainline retailers rather than traditional hi-fi dealers.
This practice may have been used to extend the lifespan of a product design that was already paid for, making sales of the Classique line a bit more profitable. They could squeeze another 6 months or more by giving the impression these were new models, when they were just a rehash.
I suspect it was also an early attempt at doing "special" models for retailers such that the differing model numbers couldn't be comparison shopped and it allowed certain retailers to avoid price matching with competitors because "oh, these are different from the one our competition is selling". Best Buy has been notorious for this practice for years, and any big retailer that has buying power can arrange this sort of thing. This happens at Home Depot/Lowe's/Menards as well with appliances, faucets, all kinds of stuff.
Chances are the A-9 and Classqie A-900 are the same unit internally, although don't discount the possibility Sansui made some minor cost cuts on the classique models causing some production changes in the process. Sevice manuals for the Classique models appear to be rare, so they may not have printed seperate editions. I don't know if Sansui providied their factory sevice centers with a cross reference list for service manuals to use on these models, but wouldn't be surprised if there was such a list at one time. A lot of factrory documentation has disappeared down the memory hole as shops closed up over the years and discarded file cabinets full of the stuff.