To shed some light on why Contra III: The Alien Wars is the fourth game in the series (after Contra Force, which really was the third in the series (and ignoring Operation C which was a Contra port)) we have to look at that crazy world of marketing and production.
Back when The Alien Wars was being developed it was scheduled to be the fourth game in the series and was titled Contra IV: The Alien Wars. An old issue of Gamepro magazine, in fact, proudly features the Contra IV preview. Contra Force was to be the third game in the series for the NES.
But things happened and games were delayed, and it became apparent that The Alien Wars would be out in stores before Contra Force would. So the numbers were switched and The Alien Wars became Contra III. However, then the problem that caused the switch in the first place was corrected and the games were swapped back to their original release dates. Unfortunately, by now it was too late to go and change Contra III: The Alien Wars back into Contra IV. Cartridges were already being produced, the advertisements were in place, and word of mouth was already starting to spread.
So Konami left it the way it was and released the fourth game in the series with the title of #3. Contra Force was released without a title number (to help cover the glitch, I'd speculate) and life went on as normal.