There are no ways. The Confederate States were arguably, at times, more Federal than the Union was, and even bordering on totalitarian in some ways.

Jefferson Davis in 1862 suspended habeas corpus and declared martial law, essentially giving him unprecedented authority which he used to his advantage. Thousands of civilians were arrested by the military throughout the Confederacy's reign. And then there is the fact that 25% of all people in the Confederacy, i.e. people of color, were slaves and could be hunted down, beaten, whipped, and more without any legal recourse. Habeas corpus would be suspended far more times by Davis than by Lincoln.

Structurally, you are also correct. It functioned with the use of a Senate, Congress, and presidential system, and in theory was little different from its counterpart whatsoever. However, in practice the Confederacy was arguably more totalitarian and as such was more of a Federal system of government than its counterpart was at the time.

In fact, by the end of the war, Jefferson Davis' administration became unpopular specifically because it had become an autocratic regime, even in the eyes of the authoritarians in the Confederacy.

So, in effect, it was arguably either very close or even more federalistic and autocratic than the Union was.

The use of the term "Confederacy" was a ploy and popular terminology that would have instilled the idea of non-federal government, but in practice, just like Nazi Germany (the Nazi party was the National Socialist party, but was stringently anti-socialist and pro-capitalist in all ways), it was really a meaningless term in application to the CSA.

Barton A. Myers, Rebels Against the Confederacy (Cambridge: Cambridge University Press, 2014)

Russell F. Weigley, A Great Civil War: A Military and Political History, 1861–1865 (Indianapolis: Indiana University Press, 2000)