Ok, this is my hip-pocket answer without looking to formal definitions, so assess accordingly:
On a scale of "Strategic-Operational-Tactical" these two constructs would best fit within "Operational."
Back when I did conventional maneuver warfare the number one question I would demand of my S-2 was: Is the enemy force oriented or terrain oriented. Knowing if he achieves his ends by destroying or neutralizing my force if he achieves his ends by controlling some key terrain regardless of the status of my force in my mind is the critical thing a commander needs to know in order to calculate tactics and assess risk.
I do not, however, believe that attrition warfare is the opposite of maneuver warfare, the key difference is what the measure of success is, not how you seek to achieve it.
If destruction of the enemy force will achieve success, then one must conduct attrition warfare. This was the measure of success between European Armies for several hundred years between Kingdoms, but (personal opinion), General Grant proved that this was a false measure in wars between Nations. He made attrition a major supporting effort (Meade's campaign with his Army of the Potomac against Lee's Army of Northern Verginia under Grant's close supervision); while his main effort was maneuver based as Sheridan in the Shenandoah and Sherman in the SE targeted the will and wherewithal of the South to continue to support the fight. I posit that if Grant had simply destroyed Lee's Army we would have slid into a period of insurgency and ultimately would have lost the Union.
Maneuver warfare is usually terrain oriented, but can be force oriented, but uses speed and firepower as both security and to achieve localized advantages over one's opponent.
Both of these are valid in State vs State warfare, where the goal is for one government to achieve a position of advantage over another government so as to force them to succumb to the will of the victor. In Populace-based warfare agreements between governments are interesting, but it is the will and perception of the populace that is controlling.
Many COIN efforts turn into a massive punishment of the populace for daring to be dissatisfied with the poor governance provided by the government. What percentage of such a populace must one kill to gain their support? Certainly you can kill them into submission, but they will re-emerge if the underlying conditions of failure are not addressed. One of the key points that I stress is that the one thing that is truly new today is that due to the information tools available it is much more difficult to "suppress" an insurgency, and one must actually seek to resolve it.
This means that when the US goes someplace, like say Afghanistan, the majority focus must be inward on fixing the government, not outward on killing the dissatisfied populace (or outward focused on killing "terrorists" like the Pakistani agents we call the Taliban, or the Sunni Arab UW HQ we call AQN. The result was the same, we ignored a fragile new governance in favor of our own objectives in the country, and allowed competitors for the sovereignty of the country to slip in behind us and compete against the government). We were literally all on the perimeter looking outward for "enemies," while the government was failing behind us inside the perimeter.
So what is the measure of success in Populace-based warfare? I would argue that it is certainly neither terrain nor the enemy combat force. It is the support of the populace itself, and once gained, must be continuously nurtured. This is the continuous duty of government.
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