לזכות ידיד נפשי משה יהודה בן פעשא דינה
לזכות ידיד נפשי ר' דוד שוקראללה בן רחל וכל בני ביתו
דאסר לה אכולי עלמא כהקדש
Kiddushin means that he forbids her to the whole world like hekdesh.
עיין לקמן דף ז'
The gemara there talks about Kiddushin "spreading" after being mekadesh half a woman just as it spreads when one is makdish part of an animal. Rashi explains the comparison is because in both cases the term "hekdesh" is used. דהא מקודשת בלשון הקדש קאמר לה - He used the term מקודשת which is a term that applies to הקדש.
ות"י נדרים ו' גבי יד לקדושין
Tosfos on the bottom margin of the page in Nedarim [6b] asks why we would think that there is יד לקדושין, that a partial use of language should be effective to create a Kiddushin? Tosfos answers that since he forbids her like hekdesh there is reason to believe that the concept of יד will apply as it does to hekdesh.
ועיקר הדבר אם עיקר על ידי שקנויה לו אסורה אעלמא או על ידי שאסורה אעלמא קנויה לו
It all depends on the question of whether because she is acquired by the husband [קנין אישות] she is forbidden to the world [קנין איסור] or because she is forbidden to the world she is acquired to her husband. If you begin with the fact that she is forbidden to the world [קנין איסור] then it make sense that Kiddushin is like hekdesh. But if you begin with the acquisition of the husband [קנין אישות] and the איסור to the world is only an outgrowth, then קנין קידושין would not have the status of hekdesh but of a regular kinyan.
וזה שני גדרים
The kinyan to the husband and the kinyan forbidding everyone else to her are two separate categories. And you can have one with the other...
A yevama [before the act of yibum] is forbidden to everyone else [קנין איסור] but is not yet married to her yavam [קנין אישות].
וכמו בקדושי חרש וחרשת לשיטת הירושלמי דרק אסורה אעלמא [מדרבנן] ולא קנויה לו עיי"ש גבי אוכלת בתרומה
The Yerushalmi [Yevamos 7/4] cites an opinion that a Bas Kohen who is married to a deaf person can eat terumah [אשתו של חרש ושל שוטה טובלת מחיק בעלה ואכלת]. The explanation is that since he never made a proper kinyan on her [even though she is forbidden to the rest of the world] it is not considered that she married a non-kohen which would now forbid her from eating terumah.
From the two examples that Rabbeinu brings where there is only a קנין איסור it seems that he is trying to prove that the primary kinyan is the קנין איסור and even in a regular case where there is also a קנין אישות it is only an outgrowth of the קנין איסור.
This discussion occurs in many places in the writings of Rabbeinu ztz"l. Hopefully we will return to this topic very soon. In the meantime here is a discussion about Eishes Yefas Toar [a careful reading will yield a serious הערה on what we just wrote]: