I'm not sure what's going on in the modern comics but during WWII, Steve Rogers was a one stripe Private, an E-2 in today's U.S. Army. "Captain" was just part of the codename for the super-hero that the government turned him into and he held no military rank as Captain America. I always wondered if Captain America did all of his 6 years of government missions for Private's pay.

And just as an FYI, there is no rank of "Commander" in the U.S. Army (or Marines or Air Force). [in the U.S., Commander is a Navy rank]. Commander is a title that a soldier can hold but it is not a rank. For example, a Captain can be a company commander. You could refer to him as "commander" to other troops but you would never address him as "commander".