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Should we merge the following tags?
If not, what's the difference between them?

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A puzzle that's stated in words, usually in terms of a story or a situation that dresses the problem up.

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A puzzle that is dressed up as a story or a longer description of a situation.

Months after this question was asked, Deusovi proposed burninating the [tag:word-problem] tag. If the tag were burninated, that would address this question. However, there has been no action on that in the past year-and-two-thirds. Until that proposal is acted on affirmatively, the proposal to merge or better distinguish these tags should remain active for discussion, as I believe it remains a valid question. Burninating one tag is not the only possible solution to this question.

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I say the two tags are not the same (although their descriptions may be quite misleading).

A in my eyes is a puzzle where the story element is crucial, and the puzzle cannot be solved without it. Phrasing, dialect, choice of words, etc. are all important when solving these types of puzzles.

On the other hand, puzzles don't have to focus on the words themselves, the tag just means that they have some story. Take for example a simple cryptogram puzzle - it's much more interesting to weave a story around the cryptogram, than just post some encrypted text by itself. The story creates an atmosphere, and gives the puzzle-creator another medium through which they can add clues.

In essence, the difference I'm trying to highlight is that the story in word problems is the puzzle itself, whilst in story puzzles, the story is just an 'added benefit' to add to the integrity of the puzzle.

Perhaps the tag descriptions could be changed to the following, or something similar:

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A puzzle that's stated in words, where the given story or scenario is crucial to solving the problem.

Related:

A puzzle of any kind that is dressed up or presented in the form of a story or longer situation.

Related:

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  • $\begingroup$ What short tag descriptions do you think should go on each, to convey that? $\endgroup$
    – WBT
    May 27, 2016 at 19:10
  • $\begingroup$ Is this distinction used in practice? $\endgroup$
    – user20
    May 27, 2016 at 19:57
  • $\begingroup$ @Emrakul it seems so, judging by the first couple of questions on each tag list. I can do a more thorough check later. $\endgroup$
    – KoA
    May 28, 2016 at 3:34
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    $\begingroup$ @WBT I've added description suggestions to my answer. Really, I'd rather have more people give their input first before any changes are made to judge whether people agree with me on this. $\endgroup$
    – KoA
    May 28, 2016 at 3:35
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    $\begingroup$ Totally agree, story generally is not a problem. For me word-problem always meant "A puzzle where you need to operate words and letters in order to solve it" and "the given words" are crucial there and hardly can be changed, not the story itself. Example is word-equation puzzles. I think one should list all different types of word-puzzle in order to figure out more clear description and may be the tag name itself, like it was done with chess tag. $\endgroup$
    – klm123
    May 28, 2016 at 6:04
  • $\begingroup$ I'm not sure these tag descriptions adequately convey the difference, especially to a user who's looking at the "wrong" one for their puzzle. How would they know there's another tag they're supposed to use instead? $\endgroup$
    – WBT
    May 28, 2016 at 12:33
  • $\begingroup$ @WBT I added a small 'related' at the bottom. The rest of the distinction should be made in a tag-wiki, not the description in my opinion. $\endgroup$
    – KoA
    May 28, 2016 at 12:40
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If you look at the actual tag wiki for (after clicking the tag, click on "learn more..."), it states:

A word problem is a problem that's stated in words, usually in terms of a story or a situation that dresses the problem up.

Although generally all problems will use words, a word problem relies on the words to make the problem interesting and relatable. An example of a word problem is as follows:

An ant crawls along the outer edge of a clock. Starting at 3:00, the ant runs clockwise from the twelve o'clock position at half the speed of the minute hand until it reaches the hour hand. It then turns back and runs at the same speed until it reaches the minute hand again. Where did the ant end up at that time, and what time was it?

The problem eventually boils down to solving a series of equations that determine how long the ant took; but without the ant to crawl around the clock, the problem would have no flavour.

From a mathematical perspective, a word problem is a mathematical problem that is stated using words instead of mathematical symbols and notation. It is not at all the same thing as just dressing up a puzzle with a backstory.

I propose that we keep both tags, but update the tag description.

Perhaps something like

A mathematical problem stated in terms of a story or situation, instead of using mathematical notation.

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