I think that many of the comments are on track for a reasonable distinction, but like everything else, black & white doesn't exist.
Let's examine my system:
(1) Focal Chorus 836v speakers. Not a "Big Box" store item, but is considered to be the flagship of the "budget" series of speakers. - Vote Hi Fi
(2) Integra 50.1. Not a "Big Box" store item, but is a multi-channel unit. - Vote Upper Mid Fi
(3) Martin Logan Dynamo 700 subwoofer. Is a "Big Box" store item and has wireless capability. - Lower Mid Fi
(4) Pioneer Elite SACD player. - I don't think it is a "Big Box" store item. Is definitely design for pure audio listening with minimal features and buttons (the main unit has three), but is designed to interface with a matching reciever. - Vote Hi Fi
(5) Integra 6-disk CD player. - Not a "Big Box" store item, but is certainly designed for convience and cannot complete with the Pioneer Elite for sound quality. - Lower Mid Fi
Overall I think my system average is Mid Fi, but having compared their sound to much more expensive products I believe I'm fairly high on the cost/return curve.