They generally designate the same player.
But there are rare occurrences where they could be different player.
For instance if you play the Morrigan, you trigger a conflict (so you initiate it) and you choose who is the instigator, so you can choose another player.
Actually, the term "initiator" is not really a reserved term in the rules like Instigator is, it is simply the player triggering the conflict.
Thank you!! This will help when we run into this!