There are two pending synonyms on MathOverflow: data.stackexchange.com/mathoverflow/query/1239539/… - stiefel-whitney $\to$ characteristic-classes and rsk-correspondence $\to$ robinson-schensted-knuth (For the latter, see also: Synonym by a moderator which needs approval?.)

The latter was the synonym which prompted this question: Synonym by a moderator which needs approval?

@MartinSleziak rsk-correspondence has now 0 question, so the synonym is probably no longer a priority. The other one is less obvious, since Stiefel-Whitney classes are particular instances of characteristic classes. The pro would be to avoid too many related tags. Also "stiefel-whitney" is poorly written and should have been stiefel-whitney-classes.

One disadvantage of synonyms suggested in this way is that no many users can vote. (And it is probably that many of those who can vote do not know that the pending synonym exists.)

If suggestions for synonyms are collected in threads like "Help cleanup tags!" or "Help improve tagging!" (Tag management 2020 on Mathematics), they are more likely to get noticed.

Another advantage of post on meta is that some discussion can take place in the comments. (And if some consensus is reached, a synonym can be created by a moderator - instead of waiting until the synonym gets enough upvotes.)

@MartinSleziak There's this law that the user's reputation on the given tag should be at least 5. This is somewhat ridiculous that this rule is the same for a narrow tag with 15 questions than for a top-level tag. It's also incoherent with the fact that high-rep users can somewhat freely edit and change tags manually, while being ultra-selected to participate to a vote.

OTOH it is true that synonym is much bigger change than just retagging.

It automatically changes one of the tags to the other one in the future - whenever somebody tries to add it or edit a question. And it cause one tag to behave exactly as the other one in the searches.

But I am probably just repeating thing you're aware of. (Especially considering that we have discussed synonyms for the deprecated tags a few days ago.)

@MartinSleziak much bigger, yes and no. I probably retagged more than 500 questions in the last few months, and this also affects searches, and I did all this using no votes (I just did it slowly enough so that I could have been stopped in case of objections). Compared to this, a vote in a decision concerning a tag with 15 questions is quite small.

... And as you pointed out, these votes are so inconvenient (hidden, with many constraints) that practically nothing occurs. And more important consensual changes such as making noncommutative-rings a synonym of noncommutative-algebra should have been done long ago.

About the question whether or not there should be a synonym between stiefel-whitney and characteristic-classes - I do not know enough to be able to tell. Anyway, since the score is at 1, at least two users thought that it should be a synonym. (Michael Albanese proposed it and it got at least one upvote.)

Anyway, the above was just a check on how many pending synonyms are there. (MO has less of them than Mathematics.)

@MartinSleziak One more absurdity is that the voting system without comments is poor quality choice for such things. If I had to vote to such a thing, I would be happy to read other users's comments (e.g., mentioning a good unexpected difference between 2 tags) , also I might like to be able to leave a comment. Do you have an idea how many synonyms have been created so far based on such underground votes?

@YCor As far as I can tell, there is only one tag synonym approved by a user who isn't the moderator: data.stackexchange.com/mathoverflow/query/1241626/… (Assuming I got the list and the query correctly.)

It is point-set-topology $\to$ gn.general-topology.

This should is the list of tag synonyms I get from SEDE: data.stackexchange.com/mathoverflow/query/1237888/… data.stackexchange.com/mathoverflow/query/1178481/…

The list of synonyms on the site doesn't show count. (Or I have missed it.)

Of course, the fact that some synonym was created by a moderator does not necessarily mean that it was discussed somewhere before that.

Looking at the above query, I could have simply checked the synonyms approved by the community user: data.stackexchange.com/mathoverflow/query/1241631/…