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.