Fur and hair're the same thing.

http://www.bartleby.com/61/74/F0367400.html

http://www.newton.dep.anl.gov/askasci/zoo00/zoo00146.htm

NB: I don't doubt that poodles are more hypoallergenic than some other dogs, including their cousins the bichon frise, but it's not because they have hair instead of fur. As for allergins, it's not the hair nor fur, it's the dander.