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It seems like there are a number of possibilities here. I had a thought that you could have a group with an executive decision-maker (leader or strategist) and someone else who is The Face (team diplomat; speaks for the group).
Often it is one person doing both of these roles, but if they were divided then it could be cause for conflict as they could step on each other's toes.
I think it's more so on the point where the two both have qualities of a leader but the difference is one is THE Leader while the other person still has a lot of dominant traits that the others tend to follow.
So they can end up stepping on each other's toes with giving orders.
Is there a trope where in a team there are sorta two leaders? Or at least someone else has leadership traits. Not to be confused with the second in command. And it can usually cause conflict. Or where two characters go "I'm the leader!"