For all the cranky ranting about "proper descriptions" of things, this thread has so far ignored the historical (and etymological) reason that some companies refer to battery banks with solar inputs as "solar generators": The Mobile Food Service Industry - aka "Taco Trucks".
The following is merely for entertainment and educational value:
Every standard step-van-turned-kitchen in North America was originally built with a generator as part of its base load-out. As the life-span of these trucks easily stretches past the service life (especially the "harsh environment service life" - aka the "abuse the snot out of it life") of the generator, most of the older food trucks are on their 2nd or 3rd generator (just as they are on their 2nd or 3rd transmission in many cases). Start with that replacement interval, then add on to that the "environmental" and political pressure that popped up when the "Food Truck" scene went from servicing job-sites to being cool places for white-collar folks to grab a lunch and hipsters to be seen waiting in line for their Korean-fusion pork-belly tacos (worth the wait, BTW), there were a lot of people complaining about the trucks running generators for multiple hours a day in areas that saw more traffic and had more political clout.
The term "Solar Generator" originally was applied to the commercial retrofit process of converting old Food Trucks by removing the entire fossil-fuel generator subsystem and replacing it with a package that includes a similarly shaped lump of batteries, BMS, etc. that bolted into the exact same spot in the generator bay. (These were usually shore-power charged but a lot of political goodwill could be... ahem... generated... by also connecting solar panels.) In the parts of the country where there is a thriving Food Truck industry, there is also a thriving ecosystem for the maintenance and upgrade of the trucks themselves. There are companies all over Southern California, for example, whose sole business is the design, specification, and installation of "Solar-powered-Battery-Pack-Generator-Replacement-Units". You can keep saying that 10 times fast, or you can explain to the guy who just wants to make his Korean Tacos that he can replace the Onan that's under his truck with a "Solar Generator" and get back to business and get the local enforcement folks off his back at the same time.