alt Hacker NewsI don't think it's necessarily a misconception but rather people having different conceptions of what the term "F-Droid" refers to. It could refer to the client, the server tools, a specific server instance, the project, the collection of applications, or possibly other things.
Some people might use "F-Droid" in the same sense as the main page [1] does, to mean "an installable catalogue of FOSS (Free and Open Source Software) applications" but others in the sense the about page [2] uses it, referring to the "non-profit volunteer project", which is consistent with the project statues [3]:
> F-Droid is the name of a not-for-profit technical, scientific and creative community effort serving the public benefit.
The documentation start page [4] makes it a bit more clear:
> F-Droid is both a repository of verified free software Android apps as well as a whole “app store kit”, providing all the tools needed to setup and run an app store. It is a community-run free software project developed by a wide range of contributors. It also includes complete build and release tools for managing the process of turning app source code into published builds.
[2] https://f-droid.org/en/about/