That's funny I always thought that a field mod was modified in the field to fit an airframe. A factory mod was one that was built at the factory and shipped to the field and just bolted on with very little work.
They start as mods in the field. If successful and someone wants to make the pitch to high command, then it could potentially turn into a factory made bolt on modification for units already deployed. Canopies would become standard equipment from the factory. Wing modifications would become standard factory equipment. Mission specific equipment like under wing armament, not so much but with the Luftwaffe it was never absolute.
Speaking of which PJ has a point, sorry I totally neglected to consider the G-10s and G-12s that were delivered with gun pods attached to the wings. Was only thinking F through G6 series.