The line between a handyman job and a contractor job isn't about size, it's about trade licensing and coordination. In Connecticut, plumbing, electrical, and HVAC work has to be done by licensed tradespeople. Framing, sheetrock, carpentry, painting, and most remodeling work doesn't, as long as the person doing it knows what they're doing.
That means a good handyman crew can legitimately handle a lot more than people assume: framing a basement, hanging and finishing drywall, replacing rotted exterior trim, installing doors and crown molding, repainting a whole house, even running a full bathroom update, as long as the plumbing and electrical portions are handled by licensed pros.
Where it goes wrong is when someone tries to do everything themselves. If a handyman offers to move your electrical panel or re-pipe your bathroom, that's a red flag. If a general contractor quotes you a full-crew price to patch a ceiling and paint one room, that's a different kind of red flag: you're paying for overhead you don't need.
The questions that sort this out are simple. Who exactly will be in my house? Which parts of this job need a licensed trade, and who's doing those? Can I get the scope and price in writing? A company that answers all three clearly, whatever they call themselves, is usually the right call.