Not like the top pic, The way I see it, the floor framing is set out 1’’ from the foundation, and the foam insulation board butts up to the bottom of the sill plate.
Top picture; Yes, very common practice where I live. My house is built that way. Two inches insulation on the foundation exterior, that leaves 3 1/2 inches of exterior wall framing bearing on the foundation. Much better drainage plain (house wrap transition to the foundation).
I live in a cold climate, but for some reason foam insulation on the exterior of the foundation is rarely done here. Perimeter drain systems are usually on the inside of the wall here.
Here in GA, that foam would be cut away between the ground and the sill plate (prevent termites and create an inspection window) So no, I do not see that offset here in my part of the woods.