IFF OBR vs FED

[Spence]

If the umpire fails to say "infield fly" and the ball is dropped, does OBR handle the resulting play differently than FED?

If, for example, the runners ran when the ball hit and a runner was tagged out, how is it handled in each?

My understanding is that the failure by the umpire to call it does not mean its not in effect and that any outs resulting from the BR running to the next base stand.

Is that true? Both FED and OBR?