While the idea of the term kiddushin stemming from “hekdesh” and reflecting the sanctity of marriage makes for a nice derasha, it does not at first glance seem that there is any conceptual relationship between the ideas. Tosfos (Kid 2b) writes regarding the terminology that “pashta d’milsa, mekudeshs li=meyuchedet li”. However, perhaps there is more to it than that. The gemara in Nedarim introduces the din of yados nedarim and debates (6b) whether a similar halacha of yad exists elsewhere, e.g. by tzedaka, pe’ah, and even kiddushin. Why should we extend the gezeiras hakasuv of yados from the world of neder to the world of kiddushin? The Ran explains that neder is a biyan av, but Tosfos writes that since kiddushin reflects the idea of hekdesh, just as yad applies to nidrei hekdesh it applies to kiddushin as well.
What is the chiddush of yad that we would not have known without a limud? I think two approaches are possible: 1) since yad is a truncated form of speech without a limud it might not count as a statement; 2) since yad is a truncated form of speech we cannot be sure of the speaker’s intent.
The Mishna in Gittin has a machlokes Rabbi Yehudah and Chachamim whether the text of a get must spell out explicitly that it is the instrument of divorce being given from husband to wife – in other words, is a partial yad-text sufficient or not. The Rishonim ask why there should be any doubt whether yad works by kiddushin if we find an example of yad by gittin. Ran answers that while the case of gittin involves passing a get from husband to wife, which implicitly demonstrates intent to divorce, the case of kiddushim mentioned in the gemara does not involve any action (the money was not handed to the women but to a different party). Just because yad works in the former case when accompanied by action, it does not necessarily work in the latter case.
The Ran’s focus on context and action as significant in revealing the speaker’s intent and validating yados seems to point to the second model of understanding the chiddush of yad, i.e. dependent on kavanah. Other Rishonim (see Tosfos Nedarim 6a who answer’s this question differently) may have a different approach.