Nitpick: a cooktop is just the burners, a range is an appliance with burners and an oven. It's relatively common on newer houses to separate them. E.g. I have a 36 inch induction cooktop and a completely separate double wall oven in another area of the kitchen.

AFAIK stovetop is also sometimes used when people mean cooktop, though in my area it's more often a casual reference to the burners of a range. I'm sure that convention varies wildly across the country.

I always just called it the stove.

I still find it very odd they call the central heating boiler/heat pump a "furnace".

A furnace is what you use to make clay set into a pot!

"Kiln"?