I usually come across some questions that include the unique-key tag, and I consider that such an expression is redundant, since a KEY constraint (be it PRIMARY, CANDIDATE or ALTERNATE), by its very nature, is supposed to enforce uniqueness of the value (or values) contained in the column (or columns) involved.
To put it another way, employing the term “unique key” is like saying/writing “key key”, “key that/which is a key”, or something of the sort.
Proper KEY tags
Hence, having appropriate KEY tags available, unique-key, being a misnomer, is superfluous in the site.
As for unique-index2, I esteem that it should in fact be a separate tag, because a unique index is a (1) physical structure, while a UNIQUE constraint is a (2) logical construct.
This meta.stackexchange.com post suggests that this kind of request has to be addressed by one or more mods, so please carry out these changes.
I would help
Naturally, if my petition is well received, I would happily help to modify the relevant questions (if possible for a non-moderator user, of course). I could suggest edits to improve the usage excerpts and/or the info of the resulting tags too.
1 Yes, I am well aware that, alas, (i) the “unique key” expression appears in the MySQL official documentation, and that (ii) a designer can set up a UNIQUE constraint by means of the
UNIQUE KEY keywords in said database management system (DBMS), but that does not imply that using that term, or the keywords, adds any value to the field of database administration.
2 Yes, (a) a unique index is commonly used as a SQL DBMS mechanism that supports (b) a UNIQUE or (c) a PRIMARY KEY constraint declaration, but that does not mean that they are the same thing —and UNIQUE and PRIMARY KEY constraints could be supported by physical structures other than indexes if the DBMS vendors and/or developers find it convenient—, therefore they should not be confused nor conflated. Besides, a unique index can be used in software products that are quite different from a SQL DBMS, where the notion of a (PRIMARY, CANDIDATE, ALTERNATE) KEY is completely irrelevant.