Basically AMOLED is one of a kind OLED, so the OLED screen has several different types and AMOLED is a type of OLED display. The word AMOLED stands for Active Matrix. Active Matrix is the opposite of previously used technology on other OLED screens that use Passive Matrix.
Differences in OLED, OLED stands for Organic Light Emitting Diode, which is a type of LED technology that uses organic methods. The advantages of OLED compared to the LCD screen is, OLED screen does not require a light layer behind the screen. Because of its own OLED layer it is able to emit a bright enough light to make the screen we can see comfortably. If you ever dismantle smarphone with LCD screen usually behind it there is a reflector layer and also a lighting layer to make the screen brighter. So, OLED technology does not require that luminous layer.