Dumb question: Is it the smaller one (that moves, along the same axis as the background stars) or the bigger one (that's fairly static). What's the other one?
The static lines are motion blurred stars (even the bright one), the small dots are radiation noise, the one that moves, with a coma is the comet.
I don't think those are motion-blurred stars. Wouldn't they have to be considerably closer to us - or Hubble going much faster - for that to be the case?
The telescope is panning to keep the comet still in the frame during the exposure.
About the bigger one that doesn't seem to move: I think it does move, it's just that it's so bright (for Hubble) that its brightness overwhelms the slight elongation of its image. In other words, it's (apparently) moving just like the other stars, it's just hard to tell.