Before we can start to answer this question, we need to understand what do they mean. I have decided to rely on etymology and linguistic meaning as they are probably the best source to describe them. Next to find out what these adjectives mean we would have to look at the meaning of noun that these adjectives stand for, ie meanings of terrorism, militancy and insurgency.
Insurgency: An active revolt or uprising. The word finds its root in French where adjective is better way to look for etymological meaning, ‘in’ means ‘against’, and ‘surgere’ means ‘to rise’, ie someone who rises against something, it does not matter whether that is violent or non violent.
Militancy: The use of confrontational or violent methods in support of a political or social cause. The word finds its root in French where the word militant it means who is engaged fighting or warfare. Hence anyone who fights or has confrontational attitude in support for a political and social cause could be classified as militant.
Terrorism: The unlawful use of violence and intimidation, especially against civilians, in the pursuit of political aims. The word finds its roots in French Revolution and Reign of Terror. This is far simplistic view of French Revolution, but after French Revolution power fell into hands of Jacobins led by Robespierre. Jacobins believed that France was surrounded by enemies all around and these enemies were working with traitors inside the country, trying to overturn Revolution. For traitors there was no court, no judges, no hearing of accused, their name on the list was enough to take them guillotine. Everyone was scared because every other day a new list would come out with names of new traitors. Soon names of several Jacobins started to feature in the list who ended up on guillotine. One day Robespierre announced he has a new list of traitors who would be dealt with. Everybody, including Jacobins were terrified as anyone could be on the list and they decided that instead of living in this fear they would rather kill Robespierre and end Reign of Terror. So that is what they did. This is what terrorism is, it is a situation where a civilian is terrified of his future, he fears the violence that could befall him or his loved ones for nothing that he has done.
Having understood the meaning of what these words means let us apply them in Kashmir situation…
Insurgents: YES, many or even most Kashmiris are insurgents, because they have risen up against India, they don’t want to be part of India. This is an indisputable fact covered even by international media that a mob rushes to save a militant during an encounter with Indian Forces speaks a lot.
Militants: YES, Kashmiris are fighting Indian State with arms and munition, so it is beyond dispute that they are militants.
Terrorist: NO because unlike Jacobin rule of France, no one in India is afraid to step out of his home, no one feels scared that he is going to die because a Kashmiri militant is going to plant a bomb or fire indiscriminately into a crowd. Hence I strongly contest calling Kashmiri militants as terrorists. In fact till 2001 WTC Attacks never had anyone called Kashmiris terrorist, they called them Militants. It was only after 2001 did Indian Army and other Government agencies started calling Kashmiris terrorists to discredit the insurgency.
Primary target of Kashmiri militants is government agents and agencies, not civilians. What terrorists do is quite different their primary target are civilians, terrorists fly airplanes into buildings (New York), terrorists fire indiscriminately at crowds (Bombay), terrorists get into schools and kill children (Peshawar), terrorists release poisonous gas in closed spaces (Japan), terrorists bomb and destroy city centres (Manchester), etc. Kashmiri militants do none of that, hence the only conclusion is Kashmiris are not terrorists. Government of India calls them terrorists because it suits her narrative in discrediting the insurgency movement, but their is no shred of truth in it. Had Kashmiris been terrorists they would have bombed railway stations, fired live rounds indiscriminately in a market, released poisonous gas in cinema halls in Delhi, Bhopal, Lucknow, Calcutta and other places. However they have not done nothing like that, hence it is absolutely wrong to call them terrorists.
And for those who want to shout Kashmiri Pandits, Yes an injustice was done to them, and yes they were terrorised and thrown out. But that was 30 years ago, today no one has reports militants threatening Pandits who have gone back and settled. So calling insurgents of today as terrorists is completely and utterly wrong. As for News Anchor Nationalists that don TV screens every night would do Pandits living in the valley a little favour if they toned down their hateful rhetoric against Kashmiris.