Strictly, villae were great slave-operated agricultural estates owned by the Roman moneyed elite which produced most of their income, and also had a large mansion they could retire to if things in the city became difficult (say, a plague struck, their political enemies were on the ascendant, or if they just wanted to concentrate on their literature).
Domus, on the other hand, were city mansions arranged around a central courtyard called atrium, where the clientes were greeted and business was conducted. They might have some cells in their front for renting as shops (tabernae), but otherwise did not represent a source of income, but only served as a residence.
Usually, when one speaks of a house, one means something very much closer to a domus than to a villa, but one could argue that Romans could and did live in villae and therefore it could be glossed as "house," although I probably never would.
Might be referring to this: https://en.wikipedia.org/wiki/Patronage_in_ancient_Rome
Basically every morning clients would visit their patrons to ask for favours/money. In exchange the clients provide support when needed. The more clients a patron has the more prestigious he is.