https://www.austrianphilately.com/field2civil/kukorkk.htm
K.u.K. stands for "Kaiserlich und Königlich", ie "Imperial and Royal". The authorities responsible for common affairs acted "imperially and royally". All agencies of the Foreign and the War Ministries thus carried the abbreviation "k.u.k.", whereby the first k stood for the Kaiser (Emperor) of Austria, the second for the King of Hungary.

K. k. stands for "Kaiserlich-Königlich", ie "Imperial-Royal". The autonomous authorities and offices of Austria acted "imperially-royally" as there were also kingdoms in Cisleithanien, for example Bohemia. They received the addition "Imperial-royal". The expression "Kingdoms and countries represented in the Reichsrat" was for a long time the only official definition of Austria! They were "k. k." up to the breakdown of the Dual Monarchy in 1918.