So let's take that for a spin. I am by no means advocating that I have some unique insight.

a.) Is CT really different from COIN in a way that usefully aids practice?
b.) Is that difference actually obvious and enduring?
CT and COIN are solutions, not the problem (actually we transformed the solutions into the problem, because they are frequently inappropriate). What we need to define is the problem, or problems? The military isn't the most flexible organization in the world, so when a threat emerges we respond with a pre-programmed solution whether it is appropriate or not. So the answer to a) is no b) is no.

Bob's World surfaced the idea in another forum, the essence of what we're doing is countering irregular threats to our national interests. They may come in the form of terrorists, financers, insurgents, propagandists, etc. The context will determine the appropriate response. You have a handful of Islamist Extremists training to blow up Greyhound buses in the mountains of W. Virgina, the response will probably be a combination of local and federal law enforcement agencies. If you have a handful of Islamist extremists training in Pakistan to target subways in NYC we may have several response options ranging from assisting the local security forces put these guys to rest (coalition law enforcement or warfare), you pay some tribal locals to kill them (UW), you can fly a UAV over them and drop a hellfire missile on them, etc. Can the response change legal character of the target from insurgent to terrorist?

If a group of financers who live in Country Y are funding Mosques and Imams in country X with the expressed intent to radicalize the attendees to participate in Jihad is that support to an insurgency or support to terrorism? Or do we have to wait and see where the attendees go to participate in Jihad to determine that? If they go to W. Virgina they're terrorists, if they go to Afghanistan they're insurgents?

If the Taliban conducts IED attacks on coalition forces and civilian targets within Afghanistan with the intent to achieve control then they are insurgents, but if they conduct an attack on a military base in Europe to get that country to pull out of Afghanistan are they insurgents or terrorists? If they conduct an attack on a subway in that same European country in an attempt to get them to pull out of Afghanistan are they terrorists or insurgents? Is it the intent of the act, or the purpose of the act that defines the character of the problem?

Let's visit the deny safehaven argument. Afghanistan was a safehave for terrorists prior to 9/11, so was the invasion of Afghanistan a CT mission or a conventional military operation where we conducted combined/coalition operations with the N. Alliance to deny safehaven to AQ? When did it transition from CT to conventional to COIN to address the same problem?

Probably terrible examples, I'm writting fast, but I'm simply pointing out that it isn't always useful to try to categorize the problem by our doctrinal responses.