If you are in the world editor and you click the first icon then all the providers will show up on all scenarios on that route, the second one you use in the scenario editor and assets only show up in that scenario. (Best Choice IMHO) and not really clear on the eye icon
I beleive the eyeball is for whether you can see it or not in the equipment list. So you can hide it from view after you use it? But don't take that to the back. I read something somewhere but it was so long ago I can't remember.