Don't confuse the name with action length. 338WM is a std 30-06 length action. The MKII Magnum (RSM) action chambered the 375 H&H, 416 Rigby and 458 Lott and is longer.
The .338 uses a medium weight barrel. The other standard action calibers now use a lightweight barrel with the possible exception of the 25/06 which I am not sure about. Yes, the 7mm now uses the lightweight barrel. So to put your .338 in another stock may require relieving the barrel channel.