I think this is mostly answered by looking them up in the dictionary

But:
What is the difference between calling it a stat and calling it a parameter?
One is the word used in RPG Maker
But seriously...in the editor, it is more accurate to use the word parameter because that number you type in
will be used by the game to calculate other things. They're commonly referred to as statistics in games you play because you're looking at the
end result of the game's calculations.
Is stat a short form of statistic?
Yes, that's extremely common in English.
Is the short form of a parameter a param?
No, not in English. But you will see it in RPG Maker's code as a shortened version referring to the word.