Strictly speaking "someone" rather than "someone else" could include yourself and it is quite permissible to say "I'm collecting this on my own behalf" so, yes, there is a difference. Most people would interpret the phrase without the word "else" in it as meaning someone other than yourself but, strictly, you should include it: "someone else's" also sounds more colloquial. I would include the ...

Context Explanation

Just because someone wills something and it happens doesn't mean there is a causal link. Likewise you can will your car to start and it still not start, no special powers involved. "Someone has forgotten their book". Why can we use 'Their" and what's the difference if instead of "their" we use "his/her"?

Insight Material

7 You can only paint someone else into a corner if they're holding your paint pot ;) To paint yourself into a corner is to, by your own action, make it impossible to get out of a difficult situation, which gets worse with every further action you take… unless you walk over the floor you've just been painting. If someone thinks they are always doing the right thing, and believes others are wrong, what would I call them? Say, for example, I did something that person considers wrong. But then on another Word for someone who thinks they can do anything, and believes ... My experience with loop someone in doesn't mean involving them in a particular physical discussion - it means adding them to the the group of people who share a piece of knowledge or are contributing to a body of work.

Final Conclusion

So "loop someone into chatting" doesn't work; "loop someone into a discussion" only works when "discussion" means an ongoing and intermittent discussion. I'm aware that run something by someone is usually used in the sense of telling something to someone to get their opinion, but it seems I've heard it used in the sense of just passing on information. If the way I used it in the sentence doesn't sound natural, what would you use instead?