Souls in TES have always interested me and now that I have learned to trust Online with its lore and found a book about soul trapping, and found trapped souls in a quest, I just can't help it, I'll have to write this little theory.
Feel free to comment, challenge the theory etc.
In the http://www.uesp.net/wiki/Online:Guild_Memo_on_Soul_Trapping it is suggested that "the Mages Guild codify and systematize the various soul-trapping magics into a common grimoire of a few reliable spells, and then teach our members that these, and only these, are the legal and authorized methods for trapping souls. Furthermore, I propose that for the purposes of soul trapping we categorize all souls into two classes..." I've found that most people believe that the souls trapped are freed when used, or the souls trapped aren't souls at all, but just the energy from souls. And I think that quote from the book proves this. There were "various soul-trapping magics", but the Guild abandoned most of them. Why? Probably, because the spells harmed the souls, or perhaps trapped the souls instead of energy. Nowadays, soul trapping is completely approved and endorsed by the Guild, so I think this gives enough reason for us to think that soul traps in single player games only take the soul's energy. While the soul traps in TESO trap the actual soul.
At least there is proof of that! In a quest called "Lost in Study", in Grahtwood, you have to search for a soul gem that contains the soul of a person. You then revive this person, and he's alive and well. (I hope that wasn't too much of a spoiler.) And that's not all about that quest; there are old soul gems there, and item descriptions say that the souls from them have dissipated. Do you think that means the souls have gotten freed, or that they have completely vanished? I'm just interested in what my soul gems do. I'm sure that you, the good people of the lore forum, understand. It's total immersion or nothing!