Middos 4:3 uses the term תאים to refer to the 38 chambers in the Beis HaMikdash.
I was surprised to see this usage, as the term לשכה appears 29 times in Mishnayos, plus another 12 in the plural, including four usages elsewhere in Middos itself. In contrast, the term תאים does not appear elsewhere in Shas. A similar pattern appears back in Biblical Hebrew: תאים appears eleven times in Tanach, while לשכה appears 41 times in Tanach. Notably, לשכה is the general term for chamber, used in both Tanach and Mishnayos to refer to the Beis HaMikdash as well as other structures, while תאים is used exclusively in conjunction with the Beis HaMikdash.
What, precisely, is the difference between these two terms? Why is one used so much more frequently; what determines when one word is more appropriate than the other?
h/t Joel K for pointing out the singular of תאים is תא, not תאה, which led me to nine other occurences of the word in Tanach (though still nowhere else in Shas, and still exclusively in conjunction with the Beis HaMikdash).