The two are correlated which does encourage that mistaken view. Github culture generally blends these two, having an open issue tracker, pull requests etc. as well as the code right there, often with a free license.

But you can very much allow bug reports and feature requests in public while developing proprietary software and you can also very much work on a project alone or with a small group without being open to random patches, contributions or requests and be open source / FLOSS.

The key definitional question is the license, not any of the cultural stuff.