I mean I think the other types do have varying levels of the alkaloids from opium, but p. Somniferum has a vastly higher amount. Although I can't immediately find statistics for that.

If you want to know more about agricultural history Kew Gardens wrote an interesting piece.

I'm not entirely sure what you mean by your last question, sorry.

There is a cultivar (Sujata) that produces no gum/latex at all. So not all poppies produce opium.

Out of the ones not gentetically engineered for more opium p. Somniferum, or the 'opium poppy' does produce the highest quantity. So it is understandable why they use the name I think; however, you are correct in that the majority of poppies can be used in the cultivation of opiates