Chemically hair in mammals is principally composed of the protein keratin, while the principle components that make up arthropod setae is chitin, polysaccharide, resilin etc.. thus giving hair and setae very different chemical makeups.
Side note - not only tarantulas have setae. Almost all invertebrates have them, and many plants have them as well.
Convergent evolution is when the same problem is faced by different organisms and similar solutions are adopted. Bats grew wings, yet they are far from birds. Mantids have eyes, but only vaguely resemble mammalian eyes. Whales have fins, but fish did it first. A major purpose of hair in mammals is sensing mechanical interactions. Well, arthropods did it first with setae. Note that first does not necessarily mean better.