The term asymmetric warfare was coined to describe activities of saboteurs, partisans, or assassins who were not clearly engaged in either war (declared nation state hostility) or terrorism (attacks on civilians, by most definitions, for media and thus political attention) activities.
For states, it justifies treating hostiles as combatants, thus killing them without the formalities of evidence, arrest, trial and sentencing. It also justifies support for friendlies engaged in acts one would avoid oneself. It also tends to suggest that, since it is 'warfare', prisoners caught engaging, or suspected of engaging, in such acts, should be considered combatants even if 'out of uniform' (there is often no 'uniform' or even consistent mark of rank).
The US and Israel coined the term illegal combatant to escape Geneva Conventions (i.e. rules) on how to treat combatants, and both have prisoners in indefinite custody without a right to counsel, trial, or eventual release. Usually there is no way or motive to cease hostility with non-state actors.
See also the Wikipedia article on asymmetric warfare.