The only time I've ever seen the terms used interchangably are from US based authors.
Not just US based authors. This gets done by AKC (American Kennel Club) and UKC (United Kennel Club, it's a US based organization not connected to the UK in any way) breeders.
To me, the quoted distinction (single coat vs double coat) makes more sense for hair vs fur than trying to use thickness of individual hairs or thickness of coverage.
Most other animals that are considered fur bearing are double coated. Mink, beaver, foxes, pretty much anything you might think of as being used to make a fur coat are double coated.
Double coated means there are two layers of hair, an under coat of courser hair that provides most of the thermal insulation, and a longer overcoat.
All cat breeds, and dog breeds that shed seasonally are double coated. It's the insulating undercoat that gets shed. They shed the winter undercoat in the spring and grow back a lighter undercoat for the summer, then in fall they shed the light summer undercoat and grow in a heaver warmer undercoat.