That's a very interesting question. It seems I have never understood it completely.
Does it mean that "дом" (as a noun) is not equal to the English "house"?
For example, I've checked both English and Russian wikipedia. The English wikipedia House - Wikipedia, the free encyclopedia provides a definition for "house" (I have underlined some key words):
"A house is a building or structure the primary function of which is to be occupied for habitation by humans or other creatures.[1][2] The term house includes many kinds of dwellings ranging from rudimentary huts of nomadic tribes to complex structures composed of many systems.[3] English-speaking people generally call any building they routinely occupy "home"."
But all the pictures in the English-language article only show some old-style (rural type) houses of 1 or 2 floors.
The Russian version of the same article (Жилище — Википедия) redirects to "жилище" (not "дом"). But I'd say "жилище" is just a more generic term than "дом". If you look at the pictures in the Russian article, you will see both old and modern houses there (e.g. Многоквартирный дом в Нидерландах, Двенадцатиэтажный жилой дом в России).
I wonder if English-speaking people never call a modern high-rise "дом" a house?
I understand it can be called "a building". But I think "a building" is something more general: it can be a factory, a museum, a hospital, a temple etc. of various architecture types.
Is it true that "a house" is reserved only for a rural low-rise "дом"? Or am I missing something?