"Shop" vs "Store": the verb usage

Solution 1:

As noted, shop, as a verb evolved around the late 17th century when "to store" was already a well-established verb with a different connotation.

Store meaning "place where goods are kept for sale" is first recorded 1721 in American English (British English prefers shop).

To store

• 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;The meaning "to keep in store for future use" (1550s) probably is a back-formation from store (n.).

To shop:

• 1680s, "to bring something to a shop, to expose for sale," from shop (n.). The meaning "to visit shops for the purpose of examining or purchasing goods" is first attested 1764.

(Etymonline)