When Namco Bandai announced Dragon Ball Z: Battle of Z they confirmed characters from the latest Dragon Ball Z movie Battle of the Gods would be in it. The game also has Cooler from Dragon Ball Z: Cooler’s Revenge and Legendary Super Saiyan Broly from Dragon Ball Z: Broly – The Legendary Super Saiyan.
Each form is considered one "character" in Dragon Ball Z: Battle of Z which explains why there are three different Coolers you can play as.
Dragon Ball Z: Cooler’s Revenge
Cooler (Ki Blast type)
Cooler Final Form (Fighting type)
Mecha Cooler (Ki Blast type)
Dragon Ball Z: Broly – The Legendary Super Saiyan
Super Saiyan Broly (Ki Blast type)
Legendary Super Saiyan Broly (Fighting type)
Dragon Ball Z: Battle of the Gods
Super Saiyan God Goku (Fighting type)
Whis (Fighting & Support type)
Bills (Fighting type)