That's at least correct for U.S. terminology (though I'd add that boilers aren't just for heating buildings, they're also really useful in chemical plants and the like to do temperature control for particular reactors, separators and the like), with a few other definitions of boilers floating around as well, e.g. steam engine boilers. For U.K. though that might be entirely different.
Where exactly this leaves U.S. boilers in U.K. terminology is an open question.