The first one modifies the gained XP based on the BR difference between the party and the monsters.
The base experience gained towards skills is 2, however there are two factors that can increase this: Battle Rank and Chain Count. This is important because half of the skill gains happens without actual fighting characters will improve even if the enemies die before they get their turn. Whenever a battle starts, skills are increased based on the commands given to the characters, and then further increased if/when the characters actually get to perform the command. Most Arts and some other actions (like regular attacks) have one or more skills associated with them which will increase when the Arts are used.
Since the developers chose to hide the experience information from the player this can sometimes be very confusing, but understanding how they work is necessary to understand how arts are learned and developed. The development of arts in the game is based on what we call skills.
