IW and Stability Operations - in your own words - what is the difference?

[Rank amateur]

But what if the what you are breaking is the what that is currently de-stabilizing the situation

Then you are fighting with the objective of getting to your stability phase. (Which makes sense, because you can not create stability until the destabilizers are gone.)

Ken, you make many good points, but I'd say that just because somebody tried to both at the same time - and it didn't work - doesn't prove that they can successfully happen at the same.

The actual process is relatively straight forward. Control the population. That takes away the bad guys "cover." You kill some of the bad guys. Some put their guns away and pretend to be civilians. You make sure the bad guys can't pick up the guns they've hidden, while easing up on the population. (You don't need to control them anymore.) Sooner or later everyone figures out some way they can live together.

I've seen no evidence that trying to stabilize a population, before you control it - before it has been cleansed of insurgents - can be successful. (But I am sure that if such evidence exists, someone will bring it to my attention and it won't be the first time that I've been wrong.)

what you suggest is abandoning an attempt to improve the stability until combat ceases. Ain't gonna happen and should not.

I suggest that you're confusing population control with stability. I suggest that the reason for similar confusion here is because you guys are too darn nice. You want to liberate and stabilize. You don't want to control. But that's the way it works. The iron fist comes first, then you can wrap a velvet glove around it. (If you wrap the velvet glove around it too soon, the iron fist becomes less effective.)