I know this may sound a rather naive question but what is the difference between the terms Homebred & Gamebred
Does gamebred mean that the horse was bred automatically by the game & had no input by the player. And homebred is if I decide which pairs to match? Or does it have something to with transferring horses between different games
As it seems obvious reading the forum that homebred horses far exceed the ability of gamebreds

Exactly as you suggest. Nothing to do with transferring between games.