There was no Grevious, because that character was created to fill in the gap that was left when they decided to kill Dooku off within the first fifteen minutes.
Obi-Wan wasn't sent to kill Grevious/Dooku either.
And it opened with a montage of the Clone Wars being fought on seven different planets, instead of the flat rescue of Palpatine.
Deciding to kill off Dooku and replace him with Grevious opened up a lot of problems, and I think ruined the story of the first half of the movie. (Which subsequently helped ruin the story of the second half.)