What if there's an umpire review and a player review on the same ball?

An on-field umpire's own referral doesn't stop a player reviewing a separate incident on the same delivery. The player can still request a review after the umpire review, as long as it's within the 15-second limit.

When both relate to different modes of dismissal, deal with the incidents in chronological order. If the first incident shows the batter is out, the ball is dead at that point and the second incident doesn't need to be looked at.

If your decision on the umpire review makes the player review unnecessary, the player review is disregarded and doesn't count towards the team's limit of two unsuccessful reviews.

Example: the bowler's end umpire refers a run out at the non-striker's end, and the fielding captain also reviews a Not out caught behind on the same ball. The caught behind happened first, so check it first; if it's out, the run out is irrelevant.