F2 drops ball on tag while blocking plate

[THREE]

Please---assume for a moment! Catcher drops ball as stated, however, the pitcher who was backing up the play reaches down and picks up ball and tags runner who is trying (as previously stated) to reach base (catcher is sitting on base and has her blocked. Would you call runner out?? What's the difference between catcher and the pitcher tagging runner? Catcher obviously has runner blocked in both cases.