Well, there are some key differences. For instance, a main one is if an organization is endemic or is sponsored by a foreign state. Also, some organizations (I'm thinking about private corporations with their own security forces) probably have far more push and pull in some areas than what the state has - the state is just a bunch of people doing stuff, and they can be corrupt, inefficient, inept, self serving, etc. You see this a lot in "failed states", but what are those exactly?
Here in Italy we have mafia and we call it organized crime, but it's really a parallel (actually, often intersecting) power structure that doesn't acknowledge the central authority and its monopoly on force. Now any decent state has to enforce its monopoly on the use of force, or else it loses authority - it becomes a failed state. So I for one would be ok calling the mafia terrorists, but for some reason it doesn't quite work that way: we assume that terrorists must be ideologically driven, preferrably by an irrational ideology at that. Mafia just wants to make money and there's little irrational about their operations, so they don't quite fit the picture. This is specific to the western point of view (which is also shaped by the idea that crime isn't always wrong) - in communist countries anyone who doesn't bend along is an "enemy of the state" - and they're not wrong, from their point of view. In theocracies, they're infidels. To what extent individualism is allowed and encouraged concurs to determine the line between what's criminal and what's not.
How many people have sheer admiration for Al Capone or El Chapo? They've glorified them with movies and TV shows. The same has been done here with the mafia - while the battle against organized crime it's still an ongoing struggle, the mafioso is romanticized - a sign of a failed state.
Now, I've also heard some americans referring to their local police force as just another gang that has the backing of the judicial system - and with civil forfeiture in mind, or the lack of a real protect and serve obligation, it doesn't sound so far fetched.
So I suppose the main difference is in the eyes of the beholders as to what legitimacy they see to any given action. To the indios in amazonia, the Brazilian state is a rogue entity encroaching on their territory. To the corporations aiming to turn the amazonias into cow fields, they're eco terrorists. In a scenario like this, the state has no choice but to enforce its rule of law, backing whoever is legally the legitimate owner of the territory, or let chaos lose.
In C2C crime units are effectively all foreign agents, which in of itself doesn't quite lend to the idea of a criminal: a criminal should be self serving, not work for a third party (any organization). If I get too many thieves and scoundrels I might consider it covert warfare and retaliate - and the AI does this too since you somehow get diplomatic penalties from killing their units and taking their cities with hidden nationality units (which I believe is a bug but a good one to keep).
In short: authority, legitimacy of power (recognized by the beholders), and the effective monopoly of force are the line breakers. Yet, most petty thieves are probably stealing because they're hungry, stupid, or both. They might have an intuition that there's something wrong with the larger picture, but most shop lifters aren't anarchists making a statement against the big man - some however will be and there's no way to know. While everything seems to be politicized today, usually occam's razor applies. It's also become a bit of a convenient excuse - "I did it because my religion/beliefs/ideology/personal contrivances made me" - I don't believe that we can take so much away from personal responsibility. Usually, if you inquire a little bit, they are acutally clueless as to what they're referring to. As much as I deeply despide the notion of wealth inequality and billionaires, I wouldn't kill one if given the chance to get away with it. I'm just not a criminal, and most people aren't.
On the other hand, Stalin was a bank robber, and most prominent progressive political figures in the XIX century had quite the police record. Criminalizing political dissent is a dangerous act by the state. On the other hand, it can't allow anything to happen helplessly or it loses authority and therefore legitimacy again. When there's an opening, then, competing organizations step in.