I got just such a coin, but I'm not sure how its face value is called correctly.
In the catalog of numists, the denomination is indicated as 1/16 Reichs Thaler. https://en.numista.com/catalogue/pieces109009.html https://en.numista.com/catalogue/pieces154260.html
But Currency - Speciedaler, and on the coin itself there is an abbreviated abbreviation:
16 Е. (einen) REICDAL. Why REICDAL - Reichs Thaler, but not REICdaler. Thaler ore Daler?
On coins of large denominations they wrote Daler at the same time:
Maybe thaler is a more German name, and daler is Danish?
I think there is not a "standard" in Numista for the denomination of the coin as it appears in the title. It may bein the local language, but it may also be in some other language that is known equally well (or better) to colllectors. So for thaler, we can find thaler, daler, daalder, talar, talara, etc. in different places the catalog
In the name I was confused not by one word, but by a combination of two words. Not Thaler-Daler, but Reichs Thaler.
I am probably new to the history of Denmark, but when I try to combine the words Denmark and the Reich, I get the same thing as Google.
And I'm starting to suspect it has nothing to do with Christian IV.