This is a somewhat controversial topic, perhaps due to different definitions.
However, here's how I understand it:
The definition has nothing to do with whether the wrist bends back or not (though it may be correlated). It has to do with whether the arm is passive and being pulled by the shoulder into the shot ("pull") vs. whether the arm and shoulder are both actively moving forward ("push").
You can try to identify these traits by looking for a lag between the start of the shoulder turn forward and the start of the hand moving forward. If there is a lag, that suggests pull. If they move simultaneously, that suggests push.
But I say "suggest" because it is possible for a player to keep his arm passive yet for there to be zero or imperceptible lag. For example, I think Jim Courier's (from the 90s) fh should be classified as "pull" even though there was no/little lag because of how his elbow was tucked in.
As for Federer, notice how his arm is basically being dragged by his body and being flung forward.
These terms are not really applied to backhands. However, intuitively, I think 1hbhs are basically pull shots in most situations.