The PE is a center mount 4x scope. It was on hex and low wall round receivers. The scope had focus adjustment.
The PEM is a side mount 4x scope based on the same scope as used on the PE, though it lacked the Focus adjustment. It was found on the high wall round receivers.
The PU is a side mount 3.5x scope. The scope did not have focus adjustment and was designed to be mass produced. Was only found on high wall round receivers. There were some early aluminum tube examples but they are rare. There is also the SVT scopes the scope tube is larger in the rear to act as a recoil lug. The svt scopes were also found on PU Mosin Nagants. They further simplified the scope to the and removed the large step in the scope tube, giving us the Pu scope that we all know and love. There were also some 6x Pu scopes one svt variant that I can't find much information on and one later Polish version built off of WW2 scopes. Note the soviets used the straight tube PU scope on heavy machine guns, a lot of time they will be painted green.

Nice picking up the K31icon, I feel everyone should have one. They are so well built, and accurate. If you are shooting the surplus save the brass. The correct berdan primers are available again. I was lucky enough to pick up a 1942 Tula ex PU sniper. Did you get a K31 that had the tag?