To my understanding the entire thing is a plan orchestrated by Big Boss.
He wakes up from his coma, and people find out wanting him dead. He disguises himself as Ishmael, and has the medic that took the brunt of the helicopter crash in "Ground Zero" "transformed" into a look alike or decoy. Ironically the medic was also in a coma for nine years.
He then takes it a step farther and has everyone convince this decoy or "phantom" as the game calls him, that he is in fact the real Big Boss. The reasoning is because Big Boss wants Outer Heaven to be a nation, and can acquire this goal with a "phantom" easier...
The Phantom goes on to making an Outer Heaven base in Africa (the setting of the original Metal Gear game for MSX) while the real Big Boss creates a base in Zanzibar (the setting of Metal Gear 2: Solid Snake). The Phantom is the Big Boss that Solid Snake fights and I guess kills in the first game, explaining why Big Boss was alive in Metal Gear 2: Solid Snake.