The difference between playing in split screen and Combat Training is the ability to have everything unlocked, including the prestige items.
The offline split screen modes for Black Ops, Black Ops II and Ghosts have the ability to play offline with AI bots. With four players, the screen is divided into four quarters, one for each player. Two players get a quarter of the screen, while a third player gets half. With three people, the screen is divided into two quarters, and one half. With two people, the screen is split in half, either vertically, or horizontally.
Split screen is featured in Call of Duty 2, Call of Duty 3, Call of Duty 4: Modern Warfare, Call of Duty: World at War, Call of Duty: Modern Warfare 2, Call of Duty: Black Ops, Call of Duty: Modern Warfare 3, Call of Duty: Black Ops II, Call of Duty: Ghosts, Call of Duty: Advanced Warfare, Call of Duty: Black Ops III, and Call of Duty: Infinite Warfare. It divides part of the screen for each player. Split screen allows multiple players to play on one screen.