That's really not the difference. You can be totally Trad in play and still take input from players. The difference is the authority structures, and how play treats that input, and really what the play is meant to be about. In Trad play, the GM retains full authority, such that input from players is suggestion, to be taken, changed, and used however the GM chooses (including ignoring or totally subverting). Further, play is centered on the exploration of the setting (possibly the plot). As such, there's a ground truth to the setting that is independent of the players -- their focus is on discovering this ground truth and then using it (or have it use them, depending).
There's a fundamental shift in approach for some other games, usually ones that use the Story Now approach to play, which are included in
@loverdrive's posting on Eastern Taxonomy as "new school" (although that school is not exclusively these games). Here, the concept of play is that the GM poses a problem, the players pose actions to deal with them, and then the system says what happens. If it's not openly established in play, then it's up for grabs. There's no 'ground truth' here that can thwart or deflect an action. If the system says success, then that action works to address the problem posed. If it fails, or a success with complication is indicated, then the GM gets to say what failure or complication looks like. These are all constrained by the premise of the game and the principles and agenda of the games in question. It's not the GM's game, it's everyone's game, and you're all playing (GM included) to find out what happens because no one could say beforehand. I noted earlier that much of mainstream play is addressing GM set goals. This kind of play is anathema to GM set goals.