1. A Navy Captain IS the equal of an Army (or Air Force or MC COL-same pay grade.
1. "Commodore" has gone in and out of fashion over the years, it has been both a rank and a position. Congress did not authorize the rank of admiral until 1862, a Commodore was the title given to a captain in command of a squadron-Commodore Perry, e.g.
2. Then as the United States began to take a more active role in world affairs and the US Navy began to "show the flag", questions of protocol made the rank of Commodore seem rather old fashioned and not quite prestigious enough.
It was revived in 1981 as part of Reagan's efforts to restore military prestige and morale after Carter, it was finally abolished in 1985.
(A college friend went in the Marine Corps in 1977, there was an attempt to revive the practice of Marine officers wearing the Sam Browne belt, went by the wayside, alas.)