In the gradebook, I understand that a red 0 means the assignment is late, but what does a grey 0 mean?
Students are still able to submit an assignment that has a black zero. A red zero indicates that they cannot submit this assignment any longer.
Under the gradebook settings for each item, there is an option that says "treat unscored as zero." That will put a black zero in for every student the moment the assignment is made active/visible. It is indicating that the assignment is incomplete. If you didn't check that box incomplete assignments would be blank. They would essentially be excused for students who don't do the assignment. A red zero indicates that the student has somehow "earned' a score of zero. Either they attempted the assignment and earned zero points, or you typed in a score of zero, or you did a bulk grade update filling in unscored items with a zero.