Mary, in my 1967 house the 2x4 stud walls are built with the narrow side of the 2x4 toward the outside/inside of the wall and the 4" sides are toward the stud cavity. In my daughters 1840 house, they are just the opposite. At the same time, the studs actually measure 1-1/2 x 3-1/2" in my house and have been planed. In my daughter's house, they are full dimension and have not been planed.
While building practices have changed over the years, I know of nothing that ever said that the 2" side of a 2x4 should run north and south. Perhaps it's just the way the wall that you have opened have been oriented. One other note is that my daughters walls are lath and plaster while mine are drywall. The total thickness of the walls in both houses works out about the same. This may have something to do with it too.