While the answer below represents the position that I held on this question at the time it was asked, and during the 18 months since, I now think that the increasing adoption of a second flagship application within ArcGIS Desktop leads me to consider that the ArcMap ([tag:arcmap]) and ArcGIS Pro ([tag:arcgis-pro]) tags should now carry more weight than than the ArcGIS Desktop ([tag:arcgis-desktop]) tag.

That newer viewpoint is presented in [my answer][1] to https://gis.meta.stackexchange.com/questions/4893  Nevertheless, I think the remainder of the answer remains valid and so I am making no changes to it for now.

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I can understand the temptation to make [tag:arcmap] a synonym of [tag:arcgis-desktop] on two grounds:

 - The ArcMap application represents about 95% of the ArcGIS Desktop GUI so they are not far from being coextensive, if only its GUI is considered.
 - Every ArcMap question comes from a user who has installed and would be using ArcGIS Desktop so it could save editors from having to later add the [tag:arcgis-desktop] tag to a GUI question that has only been tagged [tag:arcmap].

However, I do NOT think that [tag:arcmap] should be made a synonym of [tag:arcgis-desktop]

To try and explain my reasoning, I will start by saying that tag classification is anything but an exact science, so I try to be pragmatic rather than purist.

When core ArcGIS Desktop (not including its extensions) is installed there are three main components that become available to its users:

 - its GUI (mostly ArcMap but also ArcCatalog and the ArcGIS Administrator)
 - its Python bindings (ArcPy can interact with ArcMap e.g. `arcpy.RefreshActiveView()`)
 - its COM objects (ArcObjects can drive ArcMap)

The first tag that I use on a question for each of these components, respectively and usually mutually exclusively is:

 - [tag:arcgis-desktop]
 - [tag:arcpy]
 - [tag:arcobjects]

There are some questions also tagged [tag:arcmap] from each of these components.

If we were to make [tag:arcmap] a synonym of [tag:arcgis-desktop] then these additional questions would be added to the current questions tagged [tag:arcgis-desktop]:

 - [721 ArcMap questions][2] that have an [tag:arcmap] tag (and no [tag:arcpy] or [tag:arcobjects])
 - [230 ArcPy questions][3] that have an [tag:arcmap] tag
 - [288 ArcObjects questions][4] that have an [tag:arcmap] tag

To do this would I think be "over lumping" because ArcPy, and especially ArcObjects, questions usually attract a different set of answerers to the ArcGIS Desktop GUI user.

I think the primary purpose of tags is to try and help potential answerers find the questions that match their skill sets using favorites, clicking tags, etc. 

It would also mean that we no longer have three relatively "clean" self-assembling FAQs:

 - [ArcGIS Desktop GUI FAQ][5]
 - [ArcPy FAQ][6]
 - [ArcObjects FAQ][7]

because some ArcPy and ArcObjects questions would now be mixed in with those currently identified as ArcGIS Desktop GUI questions by virtue of being tagged [tag:arcgis-desktop].

Personally, I never/rarely use the [tag:arcmap] tag, because I prefer to tag any ArcMap question with [tag:arcgis-desktop] first.  If I see a question that is using the ArcMap application that has not been tagged [tag:arcgis-desktop] then I add it.  If I see a question tagged with both [tag:arcgis-desktop] and [tag:arcmap] then I usually leave both there, but because I consider [tag:arcmap] to be a low value tag (due to the amount of overlap with [tag:arcgis-desktop]) then if I think there is a more valuable tag to add then that is the one that I will remove.


  [1]: https://gis.meta.stackexchange.com/a/4896/115
  [2]: https://gis.stackexchange.com/questions/tagged/arcmap+-arcobjects+-arcpy+-arcgis-desktop
  [3]: https://gis.stackexchange.com/questions/tagged/arcmap+arcpy+-arcgis-desktop
  [4]: https://gis.stackexchange.com/questions/tagged/arcmap+arcobjects+-arcgis-desktop
  [5]: https://gis.stackexchange.com/questions/tagged/arcgis-desktop?sort=frequent
  [6]: https://gis.stackexchange.com/questions/tagged/arcpy?sort=frequent
  [7]: https://gis.stackexchange.com/questions/tagged/arcobjects?sort=frequent