There is only arena and competitive. Arena uses a new ranking system that mainly depends on your individual performance in Slayer games. While competitive is basically social (you get Credits in both).
Arena:
4 vs 4 Slayer
2 vs 2 Slayer
7 man FFA Slayer
Competitive:
4 vs 4 Slayer
4 vs 4 Objective
8 vs 8 Big Team Battle
2 vs 2 vs 2 vs 2 Multi Team
8 man Free for All
6 vs 6 Invasion