For an online game, I'd consider things like auction house, NPC shop, forum, equipment management, minigame, PvP arena, and that sort of thing to all be game modes. I'd define a game mode as one that has a distinct set of common player actions, a distinct set of relevant information, and a GUI adapted to these.
I would say those examples are sets of mechanics. A game mode has a more persistent aspect during the game play. A game mode could be two players sharing the screen, one of the players could die and the game would become single player, but the original mode selection is what matters. On the other hand NPC shops are temporary stages, unless you choose playing in the shop from the beginning, e.g. as a clerk, and you are mainly constrained to your role. That would be a game mode for a mini-game.