I feel there's a subtle difference between 'pushing thoughts out' or 'ignoring' them, and 'observing them (impassively)', which is what I've been taught when it

I feel there's a subtle difference between 'pushing thoughts out' or 'ignoring' them, and 'observing them (impassively)', which is what I've been taught when it comes to mindfulness/meditation/zen. When I meditate, my impression is not that I avoid or push away thoughts. Rather, it's as if I observe them from a distance, and inspect them, smell them, turn them over, etc. In many cases, true, these thoughts sort of dissolve of 'disappear'. But in other cases they merely change a bit in quality, or they remain with some context added. Generally speaking it's not so much about avoiding, replaying, or analyzing memories (and strengthening retention), as it is about developing and practicing discernment as to what thoughts are worth replaying, analyzing or avoiding.