I've been reading the book Montaillou, which is a historical investigation (but not tedious) into a 14th century village which held a bunch of Cathars. Quite interesting!
Anyway, turns out there is a brief discussion of the word Domus. Turns out the word is quite important; it means a physical place, a house, but also it means family. Similar to the Houses of Montague or Capulet. The idea of someones physical house being torn down is similar to breaking up a family.
In Ars I've had some of the houses as being closer than others. I wonder if all of the wizards see their houses more like family than just an association, simply because of the word meaning of Domus.
I think that certainly, magi in True Lineage Houses probably see their House as like a family.
Societates Houses don't generally seem much like families.
Mystery Cults, seems to depend on the Mystery. Bjornaer seem like an extended family/clan. Criamon and Merinita don't seem much like families: they seem to be experiences/journeys. Verditus seem more like a guild.
Indeed, the Gifted magi of House Mercere, and many of the Redcaps, are known to be an actual family descended from Founder Mercere, and many of the remaining Redcaps are also related to other Redcaps.
In our saga I am playing a magus Mercere, and make a point of referring to Cousin Guillermo, Great-Uncle Ophilio, and Aunt Alzais as appropriate, although we're probably separated by generations of divergence. Harco, therefor, is the literal Domus Magna in both senses.
The intent is that you think of the order as your tribe, your house as your family and your master/mistress as your parent. But it's a matter of personal taste in the long term.
I'm personally playing a verditius who regards his fellow magi as just as close to him as his blood family, and he's got pretty strong ties to his blood family.