NeXTStep became MacOS (OS X and later) and related systems. It does contain quite a number of BSD pieces that are now periodically pulled from FreeBSD.

The story is fun and I like telling it, strap in:

NeXTStep was basically the MACH microkernel hybridized with BSD (actual Berkley BSD before the court cases and diaspora that lead to Net/Free/Open BSD and Solaris and such) parts to make a reasonably performant modern design Unix-like, with a fancy PostScript based display layer on top, lead by Steve Jobs after he was ejected from Apple, a bunch of folks he effectively took with him, and Avie Tevanian who was the major force behind Mach when it was a research project at CMU.

Between 1988 and 1996 Apple failed like 3 times at building their own next-gen OS. Apple and IBM cooperatively fucked up the Pink/Taligent development process so hard it's still told like a ghost story to software developers, Copland got out of control with feature creep and empire building, and A/UX, cool as it was, was never going to be a mainstream OS because it contained Unix-brand-Unix and the associated thousand dollar license fee (Also IBM got involved combining some future development of A/UX and AIX for PowerPC and some of the Taligent stuff entered the picture and it turned into a clusterfuck).

So it's the mid 90s and Apple is shipping an OS from the mid 80s that they had to do hacky shit to make do even cooperative multitasking, and the executives are looking to acquire one that is already done.

Two former heads of the Mac division had left and built companies that tried to build whole computer platforms then pivoted to just selling software, Steve Jobs with NeXT and Jean-Louis Gassée with Be. The exact details of the negotiations about how they chose NeXT over Be are kind of ambiguous and vary from account to account, I'm personally of the opinion that the biggest reason is that OpenStep looked a lot like "Taligent, but not completely bungled."

So Apple Bought NeXT in 1997 in a scenario better described as "NeXT Bought Apple with Apple's Money" because all the executives in charge after the shakeup were NeXT folks.

There was an initial plan to more or less slap a OS 8 like Copland-looking GUI on the hybridized Mach/BSD kernel and most of the userland from OpenStep (an environment that at the time was called "Yellow Box"), ship it with a virtualization environment called Blue Box to run legacy MacOS programs, and call it a day. You can even play with the missing link Rhapsody from that era, and the Classic environment that early OS X versions had is the direct descendant of that BlueBox compatibility environment.

Then some of the important software vendors (read: Adobe, whose shitty development practices are why Macs are case insensitive by default to this day) revolted at the idea of having to do ground-up rewrites so Apple designed the Carbon APIs that are kind of a stepping stone between classic MacOS and the native Cocoa APIs that evolved from the Yellow Box deign which are the usual target on modern macOS/iOS.

(The story of how Windows NT - which is the underlayer of all modern windows systems - is basically "The DEC VMS team got pissed off about obviously-dumb management decisions and were looking to leave DEC while Microsoft became aware that OS/2 was failing largely due to bad IBM decisions, so Microsoft hired the core of that team to write the operating system they were designing, moved the few remaining competent folks over from OS/2 to help, and sold it as Windows" is similarly absurd. As the joke goes, it may not be a coincidence that WNT is VMS incremented).