Wireframe on shaded just allows you to see the wireframe in your viewports. So you can take a screen shot like that and not have full depth and confusing wires.
You can also turn off backface culling, but that is a whole other option which I won't go into right now as I don't exactly remember how to do it.

ANY ways, if you want to show wires using the wireframe on shaded and taking a screen should work best for ya. Cheers.