It has a tag-excerpt created by Tunk-Fey.

if these two tags are the same they should probably be synonyms.

I have pinged the (probable) tag-creator.

@MartinSleziak There's no special reason, I just want to contribute to make a tag in MSE. Indeed, brainteaser is a form of puzzle but to me and I think to the most of brainteaser lovers the word puzzle itself can also mean a toy. So I try to make a difference tag.

Brainteaser is more common to use to word problems.

BTW the tag-excerpt for brainteaser reads: Question about logic puzzles and riddles that requires thinking in unconventional ways with given constraints in mind.

This is tag-excerpt for puzzle, which was created by Asaf Karagila: This tag is meant for questions about the mathematical principles behind games, riddles, or their possible solutions. If the answer is known to you please do not use this tag to "riddle" other users, but rather to ask about the correctness of a possible solution or ways to extend and improve an existing solution.

I have copied them here so that they are not lost in case some of the tags will be removed.