From the OBR:
"FIELDER’S CHOICE is the act of a fielder who handles a fair grounder and, instead of throwing to first base to put out the batter-runner, throws to another base in an attempt to put out a preceding runner. The term is also used by scorers (a) to account for the advance of the batter-runner who takes one or more extra bases when the fielder who handles his safe hit attempts to put out a preceding runner; (b) to account for the advance of a runner (other than by stolen base or error) while a fielder is attempting to put out another runner; and (c) to account for the advance of a runner made solely because of the defensive team’s indifference (undefended steal)"
Notice it does not say an out has to be recorded, just an attempt to put out another runner.
It is technically a "fielder's choice" every time we say a runner "advanced on the throw", and there are no outs recorded many times in these situations.