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Please see WP:PRIMARYTOPIC, and WP:COMMONNAME.  A term's original meaning isn't necessarily its primary one, and we base our articles' title on their subjects' common names (when they exist), not on the official names preferred by their owners.
""Apple Store"" usually refers to the brick and mortar chain (and said chain usually is referred to as the ""Apple Store"").  A noted above, the online Apple Store (a secondary meaning) is linked via a hatnote, so it remains one click away.  The disambiguation page created by SchuminWeb merely ensures that everyone (whether seeking the primary meaning or the secondary one) must follow such a link.
If either of you disagrees that the brick and mortar chain is the primary meaning of ""Apple Store"" or that said chain usually is referred to by that name, please initiate a move request.  — "