Magasin has several meanings and is generic when referring to shops while boutique is more about small and often specialized shops.

Technically, the magasin is more the back-end storage area while the boutique is the front-end store on the street. The magasin of a shop is still sometimes called its arrière-boutique.

Note that these words come from foreign words both originally meaning “storage area”:

• Boutique comes from the greek ἀποθήκη “apotheke” so boutiquier and apothicaire are related.

• Magasin comes from the arabic مَخَازِن‏ “makazin”