It’s simple, the items you’ve got from Barrens event are restricted only to Paladins while both original Soulforge as well as Darkmoon replicas don’t have that restriction. And restrictions from the items carry over to your collection. So if you want that set on any other Plate wearer you need to buy it from Darkmoon Faire.
They made them class specific because there was one for each class. Original set, although didn’t have a class restriction it’s set bonuses worked only for Paladin and was only obrainable by Paladins so they decided when reusing it to give it a class restriction cause it’s iconic Paladin set.
Original, replica and the Barrens set all came out in different times with different design philosophies. And the transmog collection system takes all the restrictions from the item: Race, Class, Level, Specialization, Achievement, Reputation(this will be gone soon). So it matters what item you actualy collect because items with the same appearance can have different restrictions.