I mean what metric would we even use? Equipment level? Quality? I reckon it won't (or shouldn't) be profit since every miner out there is for profit.

I'd honestly just compare it to how people compare pc builders. You know someone does it seriously if they've built/customized something heavily and are always using the latest rigs/maximizing literally every part they have regardless of how good it is. I'd probably use the same here with miners, just a comparison between the quality of equipment, optimizations, etc.

I'd probably consider one a "hobby" miner if they just fired up a random rig they found in their garage and just mined whatever really. Like they probably just got the bare minimum they could needed to start mining.