Ok, just swap the order in which you check for status. So check for a completed late first, completed on time next, and so on.
Also, on first check, use this:
If (and (b2 <>"", a2 <b2),"COMP LATE",
So on first logic test, use AND ().
AND (FIRST TEST, SECOND TEST)
IF (AND (FIRST, SECOND), TRUE, FALSE)