Logically, the 'qualifying' games for a given tournament are not actually part of the tournament they are qualifying for. The clue is in the word 'qualify'.
That said, I am assuming the FA don't bother themselves with trivialities such as logic so I guess in the eyes of the FA it will be classed as the same competition.
But if it's the same competition then why call the early rounds 'qualifiers' rather than...ahem....round 1, round 2, round 3 ... (you get my drift...perhaps...)