My take on it is that she's projecting a little bit in the versions where she has the ''Diana Prince'' secret identity in some capacity. She is Diana of Themyscera, known to the world as Wonder Woman, and sees ''Diana Prince'' as merely a cover. She probably thinks the same is true of Superman - that's he's really Kal-El of Krypton and ''Clark Kent'' is just a cover.
It made sense there. In the DCEU, the whole world knew that Superman's name was Kal-El...in fact he was known as Kal-El before the name ''Superman'' was ever a thing! Also, Diana never really got to meet Clark Kent, unlike Bruce. She only met Superman/Kal-El.
That's a good take. Likewise it makes sense for J'onn to call him Kal-El, while Barry, Hal etc. call him Clark.