Yes, that was what I also said to Greg. There exist various kinds of Imitators. But the practical difference is very slight, as delivering check makes any difference for castling out of check (while normally you would castle before the opponent has any opportunity to check), and deciding whether a mate is checkmate or stalemate (while stalemate is usually only possible when the opponent's King is bare, in which case you will have many ways to checkmate that are not affected by the precice Imitator properties). So it is really a moot point.
Yes, that was what I also said to Greg. There exist various kinds of Imitators. But the practical difference is very slight, as delivering check makes any difference for castling out of check (while normally you would castle before the opponent has any opportunity to check), and deciding whether a mate is checkmate or stalemate (while stalemate is usually only possible when the opponent's King is bare, in which case you will have many ways to checkmate that are not affected by the precice Imitator properties). So it is really a moot point.