When you are on the bench, your gun pushes straight back into your shoulder and your energy dissipation tends to be back not up (watch someone shoot a 50 caliber that really is an exaggerated example)
When you are standing, the recoil goes both up and back.
Combine that with the hold on the shoulder from tight to soft, what cloths you have on and you wind up with quite a bit of difference in the barrel position as the bullet departs down range.
Bench rest shooting accurately;y depends greatly on having the same exactly pressure and if possible zero influence on the rifle (free recoil).
With my Sako Finnbear (pretty light gun in the day) , any powder change and velocity is dramatic. With the Bull barrel target rifles, much less so (the heavy barrel tends to stay down no matter what the load)
Snipers try not to shoot free hand.
Most (one exception) of the game I shot was braced.
You can simply sight in a bit low and confirm you hit a bit high. Or average it if you can or do used braced positions.
Keep in mind your hand position and your trigger work can change (almost certainly do) standing.
A sling can be used to help control that if its an issue (really not unless target shooting)