no, i think we were assuming balanced cans which splits the left and right into seperate cables such as
http/sonyglobal.scene7.com/is/image/bravia/AS0000047541_LN0000000002
what you linked in your picture is just a pair of headphones that instead of having the cable go into one earcup (then wired over to the other earcup generally through the headband) it attaches to both. on the input side (the one you connect up to devices) it still most likely is a single plug.
is it different than the standard design? (is #1 different than #2 in your photo)
no, generally not. you can think about the design being the same as earbuds. if anything i would think having two connectors would be more irritating than having a single cable to worry about but i suppose its up to preference. if you ever needed a replacement cable i think the regular design (everything to one earcup) would be cheaper.
the only case where it would be different is if it was a balanced design with seperate left and right connectors on the input side (side you connect up to the pc, phone, other said devices). i dont think you are referring to such things though.