I don't believe its a thing. You're either a good coach or not. The things that make you a good coach in the regular season are the same things that make you a good coach in the playoffs.
The idea of a "playoff coach" is just something people have made up in their heads to justify why certain teams win / lose - it makes the world simpler for them. The human brain is hard wired to look for patterns, even in the most limited of data sets.
Boudreau and Trotz are both great examples of people seeking to categorize and label things they don't fully understand. Trotz's Caps were a hot Fleury away from beating the best team of the last decade, and BB has had god-awful puck luck in game 7's. These guys were both a few bounces away from success, which would have turned the entire narrative on its head, yet here we are. Both guys have coached championship teams at the AHL level - you would think the same coaching principles that are required in an NHL playoff series would be required in the AHL, yes?
I find it funny that there is one group of people who seem to think that you need to tank to have a chance at winning, and another group who blame BB for Anaheim's lack of playoff success (ignoring the fact that they haven't tanked their way to the top). In reality, both groups are wrong, yet they still exist.