"and he shall send her away from his house": He must tell her "This is your get." From here they ruled: If one threw a get to his wife and said "Pick up this writ," or if she found it behind him and read it and found it to be her get, it is not a (valid) get until he says to her "This is your get."
(Devarim 24:2) "And she shall go out of his house": We are hereby taught that the woman leaves the presence of the man (i.e., she leaves the house, not he.)