Alph Lithograph

[RB Golbat]

Are all 4 Cards treated as the same name towards the 4 card limit in a deck or not?

And technically, since Alph Lithograph Four came out last, since they are trainer cards, should they all be errat'ed to do what Four does, or are these special cases?

 

[PokePop]

These would be more like Pokemon cards that have the same name than regular Trainers with the same name.
You are limited to 4 in a deck because they all have the same name, but each one retains its own text.
So, in this case, it would be important to specify which one(s) you have in your deck on your decklist.