The reason why I and many think the best coach is often the "most improved" is because if you go from bad to good, it's easy to lay the reason on the coach. It shows the coach was able to get the best out of what showed in the past to be a mediocre roster. If the GM had brought in a bunch of talent in that off-season, you could argue the coach instantly found a way to develop chemistry in a roster with a lot of new guys.
For your best record=best coach perspective, often you can see that a great roster will give you a great record. If that turns out to be true, then it doesn't have much to do with coaching, as is the case for Steinauer.