The Closer Mentality, Part 1: Closers in non-save situations
Closers pitch the same in save/non-save situations. You just remember it better when they pitch in a non save situation and have a bad performance.
However, I also in general we should expect closers to pitch worse in non-save situations because generally the time that happens is when they have had a lot of days off in a row and aren't sharp.
Additionally in save situations they face a random part of the lineup on average whereas when they aren't in save situations it's more likely they are brought in to face a tougher group of players.