This happens when one tag is designated a synonym of the other.

When you select both tags, this is done automatically by the system.. Based on my own experience.

I do not agree with this synonym, Navier, because the two are indeed distinct. But the self-appointed "guards of the tags", aka, the tagging police, have told me... no no no, they are the same. @MartinSleziak will likely appear and defend the tagging police's policies.

@lonestudent Actually, no. Selecting only "proof verification" will change to "solution verification".

Because there used to be, and still ought to be, the two distinct tags. But, as I said, the "Guards of all tagging" intervened to say "proof verification" ought only appear to others as "solution verification." Again, I do not think the tags are equivalent. But... the tagging police have pronounced their edict, and have been unnameable to rethinking their edict.

@amWhy I still think so. The OP chose both of these at once.

@lonestudent, I picked just proof-verification.

Sure, @lonestudent. If you picked both in your history, only solution verification will show. But for those, like Navier, who pick only "proof verification" (and not solution verification) as a tag, only "solution verification" will appear.

How can I get just proof-verification?

You can't, currently, @Navier_Stokes. That's what I've tried to express. You can contest that here, as I have contested it. But my complaint was met with complacency. I support your request. The more people who recognize the distinction in tags who object to each defaulting to "solution verification", the better the chances of change.

It's very ridiculous to me that we have a tag that can never be appeared.

I agree wholeheartedly, @Navier_Stokes!

How do I have 46 points in proof-verification and 32 points in solution-verification if they are synonyms?

Related: Why does the tag “(solution-verification)” show as “(proof-verification)”? and What is the usefulness of having “proof-verification” and “solution-verification” as different tags? I will mention that the direction (i.e., which of two tags is the master tag) was changed relatively recently.

@Navier_Stokes you are not allowed to use proof-verification. That is how it is. Accept the situation and move on. There is nothing more to discuss here. The tag has been deprecated. Just move on.