Unlike some, I do see a certain utility in "naming" various levels of conflict...if for no other reason than to restrain the instincts of some to run right for the big red button every time something untoward happens.

To me, the difference between IW and SO lies in the amount of open conflict. For example, I'd label the Indian Wars as IW, and an operation like the occupation of Germany after Word War II (or even the limited occupation of regions after World War I) as SO. Note that there is a certain amount of SO carry-over into IW (for example, the Army often performed what might be considered law enforcement-type missions during the Indian Wars, although the main focus remained on combat). Resource allocation also comes into play, although the Indian Wars sucked up almost all the active Army component at the time. Still...there was no extra mobilization (except in very limited circumstances) and no real testing of the national will or motivation (again, with a handful of very specific incidents running counter to this trend).

These are all somewhat general concepts, but again for me they serve more as a basic framework. War is war is war at the sharp end of the stick, but once you get past that I do strongly feel that there are levels of conflict and that having an understanding of them can prevent slides into a "massive retaliation" mindset.

Warfare is always in flux, and what we consider IW now might have actually been an all-out conflict by the standards of previous systems. Personally I think stability operations have the best chance to remain consistent, since they tend by nature to be more limited involvements (at least on the part of an outside power...assuming that an IW scenario isn't running at the same time - Iraq is a good example of this).

IW does not tend to be a conventional force-on-force engagement, either. There will be more limits (resources, political restrictions, weapons systems deployed or usable, etc.) and (in my mind) less tolerance for error. It's also more prone to "sliding" from one end of the scale to the other (from what seems to be SO, for example, into a larger theater-based conflict like Vietnam became) with little or no warning and possibly no action by one (or more) of the major players in the conflict.

Terms are important not just for the military, but for the people who commit that military to action. There is always flux in them (and there should be), but it's still useful to have a scale of reference.