That's a really good point. I think there's a high chance that the photos were taken from quite different locations because Hubble orbits the earth at 570km, whereas JWST is actually at the L2 Lagrangian point, which is about 1.5 million km away from Earth.
Thanks for the comments! It does look like some stars may be exhibiting stellar drift, I've isolated an example here: https://academo.org/demos/james-webb-vs-hubble-telescope-com... This is from the middle-right side of the deep field. If you look slightly below the two central galaxies, there is what looks to be a foreground star (I say that due to its brightness and the fact it has a starburst effect) and between the two frames, there seems to be a noticeable shift in position that doesn't occur with other objects.
