Currently when a user is pinged the notification message they receive says something like "ExampleUser mentioned you on ‪Wikidata:Project chat‬ in "Foobar".

This is the same whether they have been pinged individually, or as a member of a project (as done, for example, using https://www.wikidata.org/wiki/Template:Ping_project )

It should be possible for users to see under which of those circumstances they have been pinged, so that for example, they may prioritise their responses when pinged several times.

"Mentioned you" is also misleading, when it is a project, not the individual user, which has been mentioned.