I‘ve been playing a lot of Blues songs and some solos that require a lot of bending. On thing I noticed is that sometimes the players pull down and sometimes they push up when bending. I‘ve tried this out and compared the two techniques to see if I can hear any difference in the created sounds - but it seems to sound the same, no? For me I find it easier to pull down (towards the ground) on the strings compared to pushing up.
So in which situations is either technique applied? Does it matter?
Yes, pushing up & pulling down both result in the same upward change in pitch. Choosing one over the other is mostly a logistics issue.
On lower strings you can pull down more easily because there is room on the fretboard. But on the upper E string you just can't bend very high in pitch by pulling down. There's no real estate available because you'll pull the string off the fretboard! Same for the B string in most cases of a typical rock or blues whole step bend. Sometimes it's easier to do one versus the other depending on the notes that happen before or after the bend.
For example this classic lick contains both issues. You have to bend the G up & out of the way to efficiently pick the B & E strings next. And bending the B string a whole step up would pull the string off the fretboard.