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'app store' means simply 'store at which apps are offered for sale,'
Go back five years. I tell you "Someone told me that I should use iMovie to edit the movies that I made with my video camera. Where can I buy it"? You say: "You should go to an app store". I say "What on earth is an app store?"
No, that wouldn't have happened. You would have said "You should go to a computer store". "You might try a games store, they might have it". You would never have said "You should go to an app store".