Since we're citing fan-fiction, I've been working on again and off again on a piece of fan-fiction that more or less states that the differences in spellcasting between all of the games are all due to regional differences in how Magicka is channelled, with pros and cons for all of them. So, we could also chock it up to subtle foundational differences in how the spell is shaped.
And interestingly enough, according to the new novel, pieces of Daedric Princes' souls can be trapped with a sufficiently powerful item, which actually fragments the Prince (presumably until the pieces are reunited).
I would imagine trapping an entire Daedric Prince would be absolutely impossible, as the Prince is his or her realm, but to trap the spirit essence of an avatar or physical manifestation would be a powerful soul indeed.
I think the idea has been at last laid to rest, but there's been this idea that's floated around here on again and off again about whether or not it'd be possible to soul-trap a Daedra Prince. The closest evidence in favor of it was a thought that you could soul-trap his avatar, so long as you probably did it away from his realm where he could so easily change the rules on you and so long as you had something that could hold his soul. The power-sink would then manifest a new avatar, but you would contain a tiny amount of a Daedric Prince. It sort of seems that this is kind of the case, although my bets are that the man-known-as-Umbra was the Vile avatar that had been corrupted by the sword-known-as-Umbra into Umbra and then the power-sink has manifested a new avatar since then.