Yup, they are Marten and I didn't even have to enlarge the photos to know that. They are unmistakeable once you've seen a few.
Oddly enough, some trappers refer to the last set as a bird box set because it resembles a bird nest box.
I use a variation of that box that has it's opening facing down.
I've caught Mink, Marten, Squirrel, Weasel, and Fisher in that set.
And not one by catch, not even a Whiskey Jack.
I can't be sure but the first set looks like a set I call the running pole set.
No box, just two traps and half a Beaver for bait. I caught a Wolverine in a Running Pole set the last year I trapped as a registered trapper.
Here is one of my running pole sets. It's not very good photo but it was the best I could do at the time. It was nearly thirty years ago and all I had for a camera was a Instamatic 110.
And here I am with the Wolverine I took on a running pole set.
That was in 1998. I had a much better camera by then. A Canon Sureshot, 35mm film camera.
I had to tie it's legs to that log to make it look as alive as possible. It didn't really work. LOL It was my brothers idea. He wanted a photo of it in a natural pose for a sign he was making.