It may be a bit like chaos theory, but I speak four languages, and here write in English, so I don't ask too many questions...whatever gets the point across, I guess...
In English, I see "Diadem" used in close association with "circlet" because of various connotations that the word has acquired. Whatever the original meanings of these words, their use has been solidified into English along with "tiara"...I guess that in translation, one must be careful to avoid the false friend of "Diadem" for fear of sounding awkward. I usually will use "tiara" in English simply because it is the general English catch-all for diadems, bandeaux, and circlets.
But enough with the linguistics...I would also like to know if there is a particular reason for sharing jewels versus loaning them, etc. in various nations. My only guess is that it has to do with the legal status of the jewels, such as a trust that the entire collection is kept in, etc.