Here I will try to do something along these lines. Though, I recommend taking it with a grain of salt. I'm no expert in the matter. These are just some thoughts.
Why is it important?Let me give you an example. In LARP (live action role play) there are two main attitudes: play to win or to have an adventure.
In case you want to have the latter, you make a group of a fighter, spellcaster, healer, thief, etc - you know, the classic variety - and just try to have a great story together. Yes, it is great if you can also finish your mission, but the main aim is on the narrative and roleplay. You keep your real life and game separated.
In case you play to win, your approach is very different. You set up a group of clerics (essentially, tanks with healing spells) and use anything at your disposal to win the game/mission/narrative. Hence you have already made plans and preparations in advance to make sure you succeed.
You can already guess what happens when these two approaches clash within one game. Both will accuse the other of not being a good sport.
Both act based on their philosophy and expect others to do the same... and this is the problem. However, if you are aware of these two very different approaches, you can act accordingly and as a game master even make games that would challenge both. While it is wise to keep these approaches in mind, note that there are plenty of players who are somewhere in the middle.
What about in improv?I have been pondering this question for a long time. I see the difference, but don't know how to put it into words. However, it can help to look at the last 2 improv books in my collection:
The Improviser's Way: A Longform Workbook by Katy Schutte
TAKE IT EASY™ by Ryan Millar
Both brilliant in their own way and both made by brilliant improv actors/teachers (and I met both of them in my first year in improv).
One gives very specific instructions on how to create and train for a format, while the other gives advice on how to not fret too much, be like water and go with whatever is there. I don't want to call them conflicting approaches, however, one seems to be more structure oriented while the other is more about discovering what is already there. Don't get me wrong, you can also discover what is there within a structure and you can just as well create a structure around what you discover on the spot - we do it all the time on the stage.
The question is more along the lines of what do you establish first.
The Actors DreamSometimes we tend to forget what a magnificent thing we do as improv teachers. A stage is a scary place and many people have had nightmares of being in the middle of it and not knowing what to say. This nightmare is so common among people who are constantly on stage that even has a name: The Actors Dream.
We, the improv teachers are challenging this nightmare and it is not a small feat as there are only two things we can do about it. The stage is scary - you can improve the armour or remove the fear.
How do you improve the armour? By learning structure and things that work. By adding items to your toolbox for every possible situation. By being in control.
How do you remove the fear? By individual work with yourself. By letting go and being like water. By understanding that there is no such thing as failure, life is short and you will die anyway (... eh, that was me, sorry).
You can see how these two ways link to the two previously mentioned books.
Teachers or Supporters?It seems to me that we can also do the same separation on how improv is taught.
There are those who have a set rules system and way of doing improv. There is a right and wrong way to do improv and everything that does not fit their school attitude is seen as wrong.
(For example, there are people who see improv on serious topics as blasphemy - improv, in their opinion, should always make you laugh.)
These teachers are very proud of the school they participated in - seeing this as a proof that they do the right thing.
The result is that pupils know how to make a great show in a specific style of improv, however, do not often know how to appreciate other forms and attitudes.
Next to that, we also have the ones who just set a few ground rules (support and listen) and tell you to explore - be like a child and discover. Everything, (as long as you do not go against the ground rules) is permitted and fine. The scene can be on any topic, as long as you can commit to it.
These teachers have often self-learned, have experience from different sections (clowning, etc) and have combined several teachings together. The result is pupils who are better people... as the focus is more on listening and supporting skills (that are helpful also in real life)... they also have a wider view on the topic - however, it takes more time to get them stage ready in the beginning.
What I have also seen more in this way of learning improv, is that people discover more things about themselves and often pick up hobbies they used to have in their childhood - improv is still there, but more like a framework or idea that influences life, not so much as an art form that you have to perform in.
Now, I fully know that these are generalisations and just as in LARP, one is not better than the other, it just has a different focus. Most of us are somewhere in between.
However, thinking about these topics can help us understand fellow improvisers better.