Induction vs. Inducement

My wife is scheduled to be induced on Monday and the doctor refers to the process as induction. Our last doctor used the same term for the same process, and in fact "induction" is used in every relevant M.D-authored article I've read. However, when I looked up the terms in the dictionary, "induction" was defined as "the act of inducting," while "inducement" was defined as "the act of inducing." "Induct" and "induce" are two entirely different words and therefore "induction" and "inducement" are entirely different. Since it would make most sense that the docs are referring to "the act of inducing" when they say my wife is scheduled for induction, I am confused by their apparently universal use of the term "induction." All of these docs are certainly much smarter than I am, which makes me think I must be missing something. So... what am I missing here? Is she really being "inducted" when she's induced? Which is the correct term for the process of inducing labor? Thanks!