The first Call of Duty is titled, Call of Duty . The second, Call of Duty 2 . The third, Call of Duty 3 . The fourth (the one you think is the first) is titled, Call of Duty 4: Modern Warfare".
Call of Duty: Modern Warfare 2 takes place five years after the events of Call of Duty 4: Modern Warfare. During the single-player campaign, the player controls five different characters from a first-person perspective.