mid-13c., "to supply or stock," from Old French estorer "erect, construct, build; restore, repair; furnish, equip, provision," from Latin instaurare "to set up, establish; renew, restore," in Medieval Latin also "to provide, store," from in- "in" (from PIE root *en "in") + -staurare, from PIE *stau-ro-, suffixed extended form of root *sta- "to stand, make or be firm" (compare restore). The meaning "to keep in store for future use" (1550s) probably is a back-formation from store (n.). Related: Stored; storing.
c. 1300, "supplies or provisions for a household, camp, etc.," from store (v.) or else from Old French estore "provisions; a fleet, navy, army," from estorer or from Medieval Latin staurum, instaurum "store." General sense of "sufficient supply" is attested from late 15c. The meaning "place where goods are kept for sale" is first recorded 1721 in American English (British English prefers shop (n.)), from the sense "place where supplies and provisions are kept" (1660s).
The word store is of larger signification than the word shop. It not only comprehends all that is embraced in the word shop, when that word is used to designate a place in which goods or merchandise are sold, but more, a place of deposit, a store house. In common parlance the two words have a distinct meaning. We speak of shops as places in which mechanics pursue their trades, as a carpenter's shop a blacksmith's shop a shoemaker's shop. While, if we refer to a place where goods and merchandise are bought and sold, whether by wholesale or retail, we speak of it as a store. [C.J. Brickell, opinion in Sparrenberger v. The State of Alabama, December term, 1875]
Stores "articles and equipment for an army" is from 1630s. In store "laid up for future use" (also of events, etc.) is recorded from late 14c. Store-bought is attested from 1912, American English; earlier store-boughten (1872).