I don't think Winchester has ever made a true magnum action. The really long cartridges like 375 and 300 H&H are on modified long actions. There is more metal machined away from the front action ring to get the extra room in the loading/ejection port. The magazine has to be modified as well. They will take different scope mounts since the spacing on the scope mounting holes are closer together on the front ring.
But I won't swear this is right. It's been a long time since I actually held one in of the H&H magnums and only a couple at that and I could be mis-remembering.
I don't believe the above photo is accurate. The Short Magnums are exactly the same as a short action. The stock and scope mounts from my 308 and 300 WSM were interchangeable. I know I'm not mis-remembering that. The magazine follower and feed lips were different on the WSM. But the action screw spacing is the same as a short action. That is not what the above photo is showing.
