The kernel is not BSD, it's based on the Mach microkernel [1] with a BSD compatibility layer implemented on top. The whole thing collectively is called XNU [2].
It was developed from something that was based on Mach. However, it is also based on BSD, as your second link states.
> The BSD code present in XNU came from the FreeBSD kernel. Although much of it has been significantly modified, code sharing still occurs between Apple and the FreeBSD Project.
The description of "Mach with a BSD layer on top" was nonetheless accurate. When you look at actual BSD you will see it is rather un-Mac-like, so I don't think it is a highly relevant comparison. (The path drawn here from the Purism laptop to XNU is very dubious.)
[1] https://en.wikipedia.org/wiki/Mach_(kernel)
[2] https://en.wikipedia.org/wiki/XNU