Of course this is ultimately a definitional issue, but there is IMHO clearly a difference. I think rather than "mobile" the distinction might be "touchscreen only" gaming; contra some of the wild predictions I recall on HN about a decade ago, "touchscreen only" has failed to displace all other input mechanisms, because it's honestly not all that good. It works, and can be better than nothing, but I think it's hard for touchscreen to ever attain that transparent "flow" state where controls just disappear, and is table stakes for being a 'core gaming' platform.
The numbers are 13 million lite vs 85 million non-lite sales.
The mobile part is a meme, it's subsidized by the people who just want play Nintendo games (and the switch is the only/best way to do it)
https://www.nintendolife.com/news/2017/10/nintendo_gamers_pr...
Which could just as easily be fulfilled with a tablet or a phone.
And in the case of valve deck, it even has to compete with the switch in the mobile space. It's a miserable position right out the gate.
Someone better go tell the rest of the game industry they're really misallocating their resources.
Dunno about Octopath Traveller, but I have no idea why your kids are playing Captain Toad without the controller, unless you just don't trust them with the controller or something. Camera controls are clearly better with the controllers. Deemo or something like that would be a better example, but it's also clearly an exception.