Well, from my childhood, they weren't form fitted like modern diapers, just sort of a fanfold rectangular shape. Kendall (at least last time I check) still makes a similar one called Kendall Ables. This is very much like the first adult diapers that hit the market in the late 70s were like as well. It took a few years (around 1980 or so) before Attends came out with the first form fitted ones, followed shortly by Depend.
There's still some really thin plastic backed diapers, the budget end of the Wings line I believe.