Real Buildings™ generally use the latter method. This is not only because walls need to sit on the foundation rather than outside, but also because it makes exterior wall materials easier to deal with.
When you look at a wall envelope, you're combining multiple materials of bizarre sizes: 4" of brick, 3.5"-5.5" of wall stud, .25" of interior finish (drywall), etc. Interior materials (like drywall) don't need to protect against the weather, so they're weak enough to cut to whatever arbitrary size you need. Exterior materials (like brick) can't be so malleable, so they come in fairly regular sizes. (A building made of brick will probably have exterior dimensions that are divisible by 4".) As a result, you usually end up designing for an exterior wall size rather than an interior, since you can't fudge the numbers on the outside but you can on the inside.
Note that this doesn't apply to all exterior materials. If you look at a building that uses siding, usually the designed dimension is actually the structural wall, and the exterior sheathing sits on the outside. This only works because siding is easy to cut.
If you're excavating, then there is no exterior, so you'd design for interior dimensions.
If you don't do things this way, you're not "wrong" - you're basically just doing the first method but with a slightly larger foundation. If I'm working with a multi-story structure then I'll usually shrink the upper floors in to fit within the walls. The way that Real Buildings™ do this varies per structure, so neither method is really "wrong."