Peace Operations including Humanitarian Assistance (HA) and conflict prevention: military force invited or sent in to deal with a failure of the local state to deal with a crisis. This can be at the behest of international organizations or of the failing state itself although the term “host nation” seems to indicate that this is most often at the request of the state.

Occupation: A military force invades and occupies the territory of another sovereign. They become the de facto government but generally only administer government operations on a temporary basis with the intent of eventually turning it back over to the sovereign.

Annexation: A military force invades and occupies the territory of another sovereign. They become the de facto government and permanently displace the prior sovereign.
All three are apt to trigger a resistance insurgency within some % of the host nation populace. The likelihood of that growing over time regardless of how one acts, and almost immediately if one's actions are on their face illegitimate in the eyes of that population acting out.

Military stability is almost always going to be the simple establishment of some form and degree of artificial stability. A simple suppression of violence adequate to allow the rudimentary functioning of governance so long as that supppressive energy is sustained.

One key metric of if one is supporting or creating a system of artificial stability or not is to simply look at what the primary focus of security forces are. If the primary focus is to protect the government (both that of the intervening party and those they profess to be there to help) from some segment of the population, it is artificial stability. If the primary focus is to protect the people from each other so as to allow them to go about the daily pursuit of life, liberty and happiness in the context of their own culture, then it is most likely a system of natural stability that has been attained.

Many large, effective, long-stable states are artificially stable. The KSA is a poster child for this condition. China as well. These are the "Titanics": often perceived by many as "unsinkably" stable, when in truth they are quite brittle and vulnerable to rapidly sinking into an unstable or violent condition with little forewarning.