Well when you're talking about dragons their wings definitely are an extra set of arms, they're most often portrayed as bat wings in which the arm itself is mostly normal, with the fingers super-extended into struts which support the wing. Of course if you were looking for some more biological consistency they'd have either a Pterosaur like wing where one finger is hyper extended into a long rigid spar like the main spar of an aircraft wing or like a bird where the bones of the hands have fused together to form a shorter stronger wing tip. Either way, bat, bird, or pterosaur wing, the dragon's wing is definitely a limb like an arm or a leg. Dragons though in spite of having more than the usual number of limbs are still physiologically much closer to dinosaurs and birds than they are to insects. They may have armored body plates but lack a fully enclosed articulated exoskeleton, in most cases eyes much closer again to birds, dinosaurs, modern reptiles or amphibians, or mammals as opposed to insects.
In short there are a lot of other more significant physiological traits which make dragons not insect or arachnid-like.