I believe that Blaster boxes is a term started and used with gaming cards like Yu-gi-oh, etc., for boxes that contained a chunk of cards to fatten your gaming stack.
The multi-pack boxes for sport and non-sport cards were always Value boxes.
But somewhere in the last few years, blaster has taken over as the name a lot of people and stores use for all of them. (Topps still calls them correctly)
To me, it's totally wrong to use blaster, but it is what it is.