But there is a difference. A soul is the spirit of a being, which continues existing after death, possibly going on to some kind of afterlife. So, killing an animal is just detaching their soul from their physical form so they can move on to whatever comes next. Trapping their soul means they're forever bound to the gem, and unable to move on, effectively becoming imprisoned for the rest of eternity.
Well, let's not take our real-world desire/sentimets for the soul to keep existing in any form after death into the Elder Scrolls universe shall we? Nobody really knows where souls go after death in TES. They could actually be consumed by the universe itself, empowering the universe to create new souls by consuming used souls, for all we really know. Since we don't really know the importance nor substance of the soul in TES, we can't put a (real-world) morality on it imho.
But for a non-sentient being trapped in a soul gem that could actually mean it could keep on doing whatever it does for all eternity. Would it actually notice and feel bad because of that? A sentient being would become mad due to various reasons like for example the impossibility of communication with peers and being out of touch with their loved ones. A rabbit will just continue being a rabbit. Soul gems do seem capable to fulfill in basic needs, so if the rabbits has carrots which it can gather, it really don't think it'll ever care throughout eternity.