My feeling, since a survey of all relevant questions is beyond me, is that the bulk of the questions in display, output-formatting and formatting are about the same general thing, formatting output. There are also a good number about formatting input, either in
"Input" cells or
"Text" (and text-like) cells. Some are about creating a style to facilitate formatting; of course, styles and stylesheets have other uses, too. There are different levels at which to operate, from low-level boxes, to, say, the mid-level use of
Style with box options, to high-level algebraic expressions, etc.
I suggest display, output-formatting and formatting be synonyms under the tag formatting, and independent tags or sub-tags be used to distinguish important subclasses of questions of the category "making things look like I want them to." I suggest retagging be left to chance encounters of people wishing to do so.
First, I would say that the tags should make sense to a relatively new user who is search for an answer to a question. Major tag categories should not depend on too closely on hidden internal distinctions of the language and the Front End. The biggest distinction is between what the user types as input (in whatever kind of cell) and what comes out after shift-enter as output. But creating input-formatting to stand side-by-side with output-formatting seems to involve more retagging than would be feasible. Having formatting comprise both seems the most practical step at this point.
There are already input and output tags that might be used as qualifiers (although I don't suggest retagging). The tag output has a minimal wiki description; the tag input has none. There are two aspects to input, my input into Mathematica and my intended user's input into the application I'm writing. We already have the tag boxes to distinguish formatting involving the manipulation of boxes. The display seems to catch any use of "display" in English, from displaying output (or the "display" of data) to hardware displays & GPUs. The misfits could be retagged.