If a catcher has the yips and goes through a period where he has trouble getting the ball back to the mound, I think that's due to something mentally, but I wouldn't say the catcher is choking.
If a player has a critically ill child and performs poorly because of it, I think that's due to something mentally/emotionally, but I wouldn't call that choking.
If a batter goes into a slump, then that slump starts playing on his mind, causing the slump to become prolonged, there is something going on mentally, but I wouldn't call that choking.
There are players who just can't handle the scrutiny of playing in Boston. They play well with other teams, but poorly with Boston. We have seen many of those. I wouldn't call them chokers.
There are many instances where a player's performance is negatively affected by his mental state. It doesn't mean that a player choked.
All that said, I will grant you that there is a fine line here. As I stated previously, I do believe that some players are chokers. I don't believe that Price is a choker.