The translation for "daily register" is Dagsregister in Danish and Norwegian, and Ministerialia in Swedish.
The priest kept a weekly log of the sermons they preached and a daily log of their ministerial activities. These are available for some time periods. The entries could include references to the actual scriptures used in the sermons or notations, such as "Visited old, blind Mr. Bergersson today after christening the son of Lars Pehrsson at home because of illness."
Once in a great while, a note about a birth, christening, or death might be found here, which did not make its way into the actual birth, christening, or death record.