In 2005, Ed Russell and Frazer Jarvis calculated 5,472,730,538 "essentially different" 9x9 grids [1][2], once they've excluded valid grids that can be derived from another valid grid using relabelling, various permutations, reflection, rotation, etc.

[1] http://www.afjarvis.staff.shef.ac.uk/sudoku/sudgroup.html [2] (PDF) http://www.afjarvis.staff.shef.ac.uk/sudoku/russell_jarvis_s...