If you use an induction hob, a classic stovetop kettle (the kind that whistles!) will allow you to boil water quickly. The large ring on my last hob was 3kw.
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.
A furnace is what you use to make clay set into a pot!