No.
In your example of Arcade, NeoGeo and FBA let me put it this way. Arcade is every arcade game, FBA is an emulator, not a platform, NeoGeo is an arcade system and home console but all the games are arcade games, there are no differences in the home version of NeoGeo and arcade other than a limited continue system.
In the case of regular home consoles while many games have ports across multiple systems there are many times when ports are very different games such as Aladdin and Shadowrun, both are games on the SNES and the Genesis but they are very different games and not just simple ports of the same game.