I don't know if you might think that this is a waste of time but I thought it would be good to clear it up.
That being said however I find that there are still people who don't know the difference and use the two terms interchangibly, not here necessarily but certainly in other places.
I would like for someone to substantiate (or disprove) the information that follows.
Operator: A member of a military Special Operations unit.
Operative: A spy, secret agent, or detective.
Now that that's out of the way I will move onto the origin on the term operator.
As far as I know the term operative was made before the term operator. But in an article which I read 2 or so years ago (can't find it any more) it said that the term operator was created back when delta was still a new unit. Since they worked extensively with the CIA they needed to distinguish between the members of delta and CIA "operatives" to prevent confusion and so they began calling delta members "operators".
This is apparently how the term operator came to mean a member of a military special ops unit and/or LE SWAT and an operative being a member of an intelligence agency.
In a wikipedia article about delta there is a section that has parts that agree with and others that disagree with the article I mentioned before. And yes I know it's wikipedia but still. And here is the quote:
The Term "Operator"
Inside the United States Special Operations community, the term "Operator" describes one specific individual – a Delta Force member who has completed 1st SFOD-D’s selection for "Operators" and has graduated OTC (Operators Training Course). “Operator” was first used by Delta Force to distinguish between “Operational” and “Non-Operational” personnel assigned to the unit. Other Special Operations Forces (Special Forces, Rangers, PJs, and SEALs) also use specific names to describe their jobs (Army Rangers, Navy SEALs, Air Force Pararescue, CIA Operatives, FBI Agents); "Operator" is the specific term assigned to Delta’s direct action operational personnel: Delta Force Operators. However, since the early 2000s other Special Operations Forces have also adopted the term “Operator.”