You can insure against possible negative outcomes of someone else's contracts.
e.g.) Party A and Party B sign a contract that Party B will pay Party A $X by some date. Party A has seperately agreed to pay you $0.9X shortly afterward.
You are a savvy businessperson and realize that Party A will not have $0.9X to pay you if the Party B fails to make their payment.
Party B is on the rocks after a nasty reorg, and you think the probability they fail to pay is significantly greater than 0.
You want to protect your business against this event. To do so, you purchase a Credit Default Swap from Party C for $0.05X that ensures the full $0.9X payment.
While Michael Barry was "speculating" using CDS's, you could also argue that he was "insuring" his firm against a housing crash, which did tank most investment vehicles.
I buy a house at a higher-than-usual price for the area, expecting its value to increase because of some development that is occurring nearby—an automotive manufacturer has recently agreed to build a plant about 10 minutes away, creating around 2000 jobs in the area.
However, the deal still needs to be approved by the Feds. If I wait until the approval, the house might cost even more to buy and potentially make my investment unprofitable (or not profitable enough). But if the plant is not approved, my house will likely not gain enough in value and I will have paid too much.
To insure against the Feds not approving the plant, I can by a CDS against that risk. I will lose a small amount of profit in my eventual sale of the house to pay for the CDS, but will also prevent a large (profit) loss in the event that the plant is not approved.
Note: In this example, I do not have any direct interest in the (future) plant, or the auto manufacturer, and I obviously do not control the actions of Federal regulators. Nevertheless, I am exposed to risks (and benefits!) taken by them as a homeowner in the area, and a CDS can be used to insure against those risks at minimal cost.
Admittedly, this is fairly sophisticated for an individual homeowner, but this kind of thing is routine for financial professionals. CDS is a kind of insurance, and it's totally legitimate, even though you are usually not insuring something you have a direct interest in.
Of course, this is just my own personal subjective consideration. Not related to the official definitions of these terms at all.