The living room is more than just a small home teaching room. Open floor space with a couple of nice chairs, the piano, and a large modern/sleek sectional.
Family room is more relaxed and gives us a space for the TV, a couch and love seat, and a spot for the kids’ terrariums.
When we invite crowds over we can spread out a bit or have kids in a different area with different activities.
I’m sure I get my preference from my upbringing where we had a home full of kids and all their friends. It is nice when my son has his friends over while my daughter has hers over. Plenty of space and separation for everyone.