I've been edging away from the "storytelling game" (group or otherwise) framing of things for a while now. It's... well, it's not wrong, but I've found that the framing centres things like plot and even performance in everybody's mind, and that has had some perverse side effects. It negates the collaborative effort in peoples minds, linearising the game, and shifting agency away from the PCs and the table, and to the GM during prep.
It's the connotational difference between "telling a story" and "running an adventure", and it's mostly invisible.