A difference could be created, but doesn't exist in current usage
The most natural distinction to apply comes from the excerpt for voting-systems which states that it is "Not for questions about country-specific rules". A natural conclusion is that a different tag could exist for country-specific rules, and electoral-system seems suitable to me.
However, current use of the tags doesn't support that distinction. Right now, questions about voting/election theory and questions about country-specific voting/election systems exist in significant numbers in each tag. Trying to create such a distinction would split both tags and require a lot of manual retagging. Instead I think it's appropriate to simply unify the tags.
In terms of which tag should be the "main" one and which should be the synonym, I would usually go with leaving the more popular tag and making the other a synonym, but in this case I have a slight preference for electoral-system. The main reason is that the Wikipedia page for "Voting system", which is currently linked on the voting-systems info page, redirects to the "Electoral System" page; Wikipedia isn't an authority on the subject, but it would be nice for the tag names to reflect the concepts we link to describe them. It's only a slight preference though. I would also remove the "Not about country-specific rules" part of the usage guide.
TL;DR The tags are the same in current usage, and merging them seems more beneficial than creating an artificial divide.