All of them are understandable, so probably all are valid. Pinball machine is the official term, but all the others are essentially abbreviations or remixes.
I've also heard the term "flapper game" a few times, but that usually comes from someone who really isn't very familiar with pinball.
In some parts of Europe (such as Germany), they're called flipper games/machines. It's interesting that they decided to name the game after the flippers, rather than the ball like in the US.