As Exotion pointed out, the 20333 does have a curved plate. I checked Toro.com's Parts (similar to ereplacementparts.com) and it clearly shows that this mower has the aluminum blade support that is curved (how could I have forgot!)
The 20333 uses 2 studs with nuts to secure the blade, versus the 20073 which uses one bolt.
Either way, Toro.com's parts section calls for the same blade for both mowers! I guess it is possible that I was WRONG and that both mowers do infact use the same blade! I will take photos this weekend when I go to check out my Father's mower, to solve this dilemma once and for all.