Perplexing Mishna

The first mishna in Kiddushin talks about a woman being kohah herself from her husband through get or missas ha-baal. At the end of the mishna we learn that a yevama is konah herself with chalitza or missas ha-yavam. Now the kinyan in the reisha is much different than the kinyan in the seifa. In the reisha she is already knuyah to the baal and now is released. In the seifa she is knuya to no one. So how does the lashon "kinyan" of the seifa "shtim" with the reisha. [This was asked by the Rashash and he was "beaten to it" by the Tofos Ri"d]

A few notes here.