[Spivak]

Forbidding commercial use doesn't make something closed source but it does make it proprietary. The compliment of Open Source isn't closed source.

[ramshorns]

Can you give an example of something that's neither open source nor closed source, or of something that's both open source and closed source?

[Spivak]

Gitlab EE is one.

Not closed source since the source is public and freely given [1]. Not open source because the license [2] forbids use based on field of endeavor which is required in the OSD [3].

[1] https://gitlab.com/gitlab-org/gitlab-ee [2] https://gitlab.com/gitlab-org/gitlab-ee/blob/master/LICENSE [3] https://opensource.org/osd-annotated

Not that Wikipedia is a source of truth but it does corroborate that at least some other people agree with this analysis [4].

[4] https://simple.wikipedia.org/wiki/Closed_source

Edit:

As for the other direction, you can't have software be Open Source and closed source simultaneously since being Open Source requires the source to be available. Or in symbols.

Free Software ⊆ Open Source ⊆ source-available

closed source ∪ source-available = 𝕌

closed source ∩ source-available = ∅

[gnulinux]

Commons Clause is neither open source nor closed source; it is proprietary. Something cannot be both open source and closed source.