Quoted from vid1900:Your command of the English language is probably better than mine, but what you are describing sure sounds like a laminate.
For instance, "Laminated Insert Decals" are sheets of plastic, printed with ink on the backside, then a layer of adhesive is rolled over it.
Its like a translite, reverse printed on a type of Polycarb die cut, with a removable adhesive liner like a sticker
the higher quality print is probably not running the art via next gen which creates the dots