Urim and Thummim are lots in the pouch of the priests (High Priest? I don't remember) in the Old Testament. Not sure what "lot" is in this context but I am imagining some kind of dice. In any case, sometimes the lot were cast and the result seen as manifestation of divine will. Revelation.
The interpreters (on the breastplate which Joseph Smith got together with the plates) were clear stones you would look into and see something. Joseph Smith used them to translate the Book of Mormon, and I suppose there could be some other revelations he had through them.
The connection is both are physical objects used to inquire God and receive revelation, but that's about it. It's not even obvious whether or not the Urim and Thummim were stones (right?). The interpreters are more like the Liahona than the Urim and Thummim in my mind. The Book of Mormon, as far as I am aware, doesn't use the term "Urim and Thummim", nor does any angel that visited Joseph Smith (right?). The interpreters appear in the Book of Mormon from nowhere, as far as I am aware, King Mosiah just happens to have them.
So why did (I assume Joseph Smith) start calling them "Urim and Thummim"? Just to give them a biblical name or is there something more to it? And when did this association start?