Congressional Medal Of Honor
It's a shame to see your link has US military personnel identifying it as the "Congressional Medal Of Honor", they should know better, its correct term is "Medal Of Honor", nothing Congressional about it, It is presented by the President of the United States, in the name of Congress, which seems to be the source of confusion. You will see no mention of "Congressional" in official US military documentation.
The secretary of the Army, on behalf of the Department of Defense, has testified to Congress that the term "Congressional Medal of Honor" is "incorrect" as a matter of statute, and that "it seems inappropriate to modify the name of the medal with the word 'Congressional' as each award is made in the name of the Congress, through a mandated process in the military chain of command, not 'by' Congress, and there is no other Medal of Honor, so no need for the modifier.