Predators of different species competing for the same prey is called competition.

The answer is 'inter-species competition'. This is when different species in the same environment complete for the same resource. Examples can be trees in a dense forest competing for sunlight. Those trees able to grow the fastest and tallest will break through the forest canopy and receive the full sunlight. Another example are large predators of different species living on the African Savannah environment, such as lions and leopards, which would be competing for the same prey animals.