Seems like at #fdroid we started to tackle a problem which I personally also encountered, but never found a good solution in my head: the distinction between F-Droid (the repository of FOSS apps) and F-Droid (the client for repositories of android apps). See https://gitlab.com/fdroid/admin/-/issues/469 (thanks @uniqx for bringing it up)

It basically the #NamingThingsIsHard problem, you always have in technology

F-Droids repo could use a name (#469) · Issues · F-Droid / admin · GitLab

F-Droids central repository and the F-Droid client app are very distinct things, yet we refer to them under the same name. This makes it very hard to explain...

^GitLab