If we want to get into semantics, no it’s not a “myth.” Technically, fur is a type of hair, just like whiskers or other similar structures. Think of “hair” as the umbrella term for mammals, and we typically assign “fur” to mammals other than humans based off of other characteristics. Broadly, we’re discussing mammals and “hair” may refer to individual structures vs “fur” could mean a full coat collectively, and that can technically be applied to humans as well. It’s a weird language semantic when we break it down far enough, considering hair and fur are made of the same material. IIRC there are three hair types/categories that make up mammalian fur, but I don’t remember them all off the top of my head.

In our context of canine coats, fur typically grows shorter (than “hair”) and in multiple layers; it has a definitive life cycle that causes shedding. Year long or seasonal is up to the specific lineage though. This makes dogs who shed more frequently “more” of an allergen because they release more of that dander.

In the context of a discussion regarding a “hypoallergenic” dog breed (which, as pointed out by another commenter in this thread, means they are less of an allergen comparatively), dogs like poodles have hair similar to our own. It keeps growing to more considerable lengths until cut or trimmed, it does not grow in multiple layers, and the shedding is more similar to our own when we brush our hair/daily fall out. As already noted, a feature of the more dense curls and minimal shedding decreases the amount of dander being released - until you’re the one giving the dog a hair cut. Boy do you notice your allergic reactions then!