[Azrael3000]

There's no drifting there. What you are seeing is gravitational lensing. The light of (most likely a galaxy) is bent around another galaxy or star which distorts its appearance. Also this means it can potentially show up multiple times on the image (e.g. opposite side w.r.t. the lensing object)

[outputchannel]

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.

[gliptic]

Yeap, this is very likely proper motion. That star is in our galaxy.

[shmageggy]

I was wondering how you made that gif and looking for an option on the UI to automatically export one, but then I realized you are OP. That would be a cool feature to add.

[q1w2]

It might also be caused by parallax. The image might have been taken at different points in the Earth's orbit around the sun.

[outputchannel]

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.

[Azrael3000]

Fair enough, I misinterpreted GPs post. He and you are obviously correct.