Family Room = more casual, where the TV is.
Living Room = nicer, no TV, don't spend a lot of time there. (so why is it the living room?)
If you had to define the two rooms according to how it is in our house:
Family Room = TV, comfy couches, Tanner's office, nicest room in the house
Living Room = grandma's old piano and Tanner's sport court
My kids might have a harder time differentiating the two...
Our house is pretty big for the two of us (we don't use the up or downstairs). So when we moved in I wasn't interested in spending the money and time to furnish all the rooms. We were so blessed to have most of our furniture gifted to us or lent to us. So I left our living room untouched, until we got some furniture for it...
My grandma moved and we got her old piano, which I love to play from time to time.
And plus, I think it keeps us young. :)