I cannot speak for uses outside North America, but on this side of the pond, the word dealer is highly contextual. If someone remarks I don't bring my children over to their house, because his nephew is a dealer, she is probably deferring to a drug dealer.
For the average American, however dealer almost always refers to a car dealer. From my limited exposure to that world, people who buy illicit drugs tends to other euphemisms like their "source" or their "guy" or their "supplier," if the relationship is good, their pusher or dealer if there is an admission the relationship is bad. Dealer on its own is softer than drug dealer; if you call someone a crack dealer or meth dealer, it's effectively an insult, as these are very low status professions widely considered among the worst elements of society.
The AHD definition is telling in its examples—
One that is engaged in buying and selling: a used-car dealer; a drug dealer.
It must be said, there are negative connotations of car dealers, especially used car dealers, as well. They have a reputation for aggressive or dishonest sales practices and for overpriced or unnecessary maintenance services. This has led some car companies (especially from premium marques) to push the terminology pre-owned instead of used and retailer instead of dealer, though I do not believe they have widespread currency among the public.
All in all, however, you would probably want to avoid dealer not because of its potential social baggage, but because it is not commonly used outside of a few products. You might buy artwork from an art dealer, or a yacht from a boat dealer, but at the consumer/retail level there are few other products bought and sold by a dealer. I cannot think of any kind of store (AmE) or shop (BrE) one would refer to as a dealer, except in jest to compare them to a drug dealer.