This terminology is backwards. The individual folders were "Trappers," so named because the vertical pockets tended to "trap" papers inside when they were dropped (unlike Pee Chees, for instance). The "Trapper Keeper" was the 3-ring binder that you kept all your Trappers in. I never had a Keeper, but Trappers fit in more ordinary 3-ring binders, too.

(I note that Mead now seems to brand the folders themselves as "Trapper Keeper," further muddying the waters.)

I used Trappers for a time in middle and high school, but later used ordinary Pee Chees. By college, I was using Pee Chee-like folders I got from the university bookstore, with the university logo on them. I think the issue we had with Trappers was that they were more expensive than the other folder types.