They mean different things.
- Inside-right is a historical designation and implies a particular system and the inside-right's relationship to the other players in that system.
- Inverted-winger is specifically a winger who plays on the side opposite his stronger foot, usually to allow the fullback to exploit the space out wide. The position still demands certain of the traditional qualities associated with wingers like speed, dribbling, and agility.
- False winger, going on the analogy with false nine, is a term that emphasises the intention to cause uncertainty in the opposition, whether the fullback tracks the winger or not and who should pick him up. You can play Mata on the left as a false winger, but he wouldn't be an inverted winger.
- Wide playmaker I haven't heard so much about, but it seems to imply an opposition to winger, i.e., a wide playmaker is not the fastest, he doesn't run down the flanks and get to the byline, he drops back to pick up the ball from deep, etc.
- You missed the inside-forward, wihich is a goalscorer who starts out wide/in the channel and comes in looking to score, like David Villa during his la
st good period.