Git's "ours"/"theirs" terminology is often confusing to newcomers, especially when from a certain (incorrect, but fairly common) point of view their meaning may appear to be swapped between merge and rebase. I think in an attempt to make the terminology less confusing UIs tend to reinvent it, but they always fail miserably, ending up with the same problem, just with slightly different words.
This constant reinvention makes the situation even worse, because now the terminology is not only confusing, but also inconsistent across different tools.
We use SVN at work and it's a nightmare there too, "mine" and "theirs" and whatnot. I frequently end up looking at historical versions just to verify which is which.
If I have a merge conflict I typically have to be very conscious about what was done in both versions, to make sure the combination works.
I wish for "working copy" and "from commit 1234 (branch xyz)" or something informative, rather than confusing catch-all terms.
Using SmartSVN which makes life a fair bit better but still keeps this confusing terminology.
We'll be migrating to Git this year though so.
For reference, the codebase is over 20 years old, and includes binary dependencies like libraries. Makes it easy to compile old versions when needed, not so easy on the repository size...
I think even presenting them as options makes it even more confusing to newcomers. Usually I find that neither is correct and there's a change on both sides I need to manually merge (so I don't even pay attention to the terminology), but I've seen co-workers just blindly choose their changes because it's familiar looking then get confused when it doesn't work right.
This constant reinvention makes the situation even worse, because now the terminology is not only confusing, but also inconsistent across different tools.