AppiumDriver: This driver class inherits from the RemoteWebDriver class, but it adds in additional functions that are useful in the context of a mobile automation test through the Appium server.
AndroidDriver: This driver class inherits from AppiumDriver, but it adds in additional functions that are useful in the context of a mobile automation test on Android devices through Appium. Only use this driver class if you want to start a test on an Android device or Android emulator.
IOSDriver: This driver class inherits from AppiumDriver, but it adds in additional functions that are useful in the context of a mobile automation test on iOS devices through Appium. Only use this driver class if you want to start a test on an iOS device or iOS emulator.
As you can see, the drivers and their names tie in closely with what they do. When it comes to initializing a driver, only use the Android or IOS drivers.