
The three door version is defined following the Wikipedia article: https://en.wikipedia.org/wiki/Monty_Hall_problem
The 1000 door variant differs in that there are 1000 doors, 999 with a goat and one with a car. After you pick a door, the presenter opens 998 doors revealing 998 goats, leaving you with two closed doors: the one you picked initially, and another one.
The addition of extra doors helps clarify that you 'open all doors but 2', rather than 'just open 1 door'.
In the 3 door case, these two actions are the same, but the 1000 door case makes them very different.
By opening so many doors, it makes it a bit more obvious how the host's knowledge (Monty's knowledge) factors into the circumstances of the bet, and that he's helping narrow things down for you.