Not a lot of difference between the two.
I just found myself in the same position, only reversed, & found another difference you didn't encounter.
I just bought a 3556TSW (9mm) this weekend, in seemly unfired condition, & it included everything except a second magazine.
Not having any full-sized double stack 9mms in my collection to borrow a mag from, on a whim, I tried a mag from one of my full-sized double stack 40s in it.
Rounds feed & ejected fine (manually cycling) until the last round. It never feed because the slide would lock back with the last round still sitting on the follower.
The difference, & problem going from 9mm to .40 I found, is that while the relief notch on the left side of the follower, to push up on the slide stop lever, are of difference depths (the 40's notch is ~.004" deeper than the 9mm's), the last 9mm round is pushed up higher because the 40's magazine's lips are wider causing the follower to push up the slide stop lever just enough to lock back the slide back before the last round is picked up every time.
.