Answer: You can find the full answer on my Dog Blog at this link:
Short answer follows:
This is sort of a true AND false answer. Fur and hair are really the same thing. There are many different types of hair, but they are all basically made of similar material, though they vary in function and growth pattern/rates. A "fur" coated dog is one that has several layers to the hair coat. Some of these hairs shed with temperature and light changes (seasonal), and this can really aggravate allergic reactions in people. For this reason, a single-layer hair coated dog (such as a cockapoo) is preferable for those with non health-risking allergies to animals.
So, "fur" essentially has different layers to it, some that are seasonal, and a "hair" breed wears the same coat all year round.
The term "non-shedding" is true for a cockapoo that meets standards, but it is very often used to mislead people... and the use of the word "hypoallergenic" for dogs is really NOT true. This term is accepted by the community, however it really is misleading, and as a medical professional I really object to the use of this term!!
The definition of hypoallergenic is non-allergy producing. It is a term applied to "a preparation in which every possible care has been taken in formulation and production to ensure minimum instance of allergic reactions" (Blakiston's Medical Dictionary).
So the short of it is my dogs don't shed seasonal coats like some dogs do, but they do lose hair occasionally. They are not hypoallergenic, as no dogs are, but they are low dander and there is a lower-risk of allergies associated with this kind of dog.
I hope this answers your questions! I do have a post that is more detailed about allergies if you'd like to read more about allergies in particular (different link from that posted above):