Homage?
My dictionary defines pastiche as “an artistic work in a style that imitates that of another work, artist, or period”, so there you go!
[It also defines it as “a confused mixture or jumble”, so there you go!]
^Well, that does cover quite a bit of ground.^
I generally see them listed as “guest authors,” or if it’s a setting that isn’t written primarily by one author any more, as a “shared world/setting.”
Funnily enough, some of those published anthologies in a specific world (Thieves’ World is one, and the Borderland setting written/edited by Terri Windling, and the Honorverse by David Weber) contain instances where the other authors were WANTING to write in the other person’s playground, and in some cases even already wrote unpublished “fanfic” of their own that they just kept to themselves until it came out that the main author/editor was looking for contributors to an anthology. Then they polished it up and sent it in for consideration.
In other cases, the author hasn’t yet allowed anyone else to play in their playground, but other authors have publically expressed their interest if/when it happens (Jim Butcher’s Dresden Files is one that comes to mind, as does Brandon Sanderson’s Mistborn setting.)
In the Honorverse instance, two of the more interested “guest authors” from the various anthologies actually became major writers in that universe because of their interest and their wanting to continue to write in that world. Jane Linskold is handling the writing of the YA spinoff series, and Eric Flint handles books and short stories that deal with a set of royal and spy recurring characters.
Just you wait - give it another 5 to 10 years, and there will be scholarly dissertations written on the craft and benefits of shared worlds, guest-authoring, and “fanfic” writing for building relationships between various authors and publishing houses, encouraging cross-pollination among the fandoms, and improving the writing craft of the authors.