Similar situation for *BSD on the iPhone/iPad/iPod touch, it is a golden age for Unix/Linux but, like you say, invisible to the end-user.
The Darwin portion is for most intents and purposes based on BSD -- particularly FreeBSD-- running on top of XNU (a hybrid Mach 3.0 microkernel with big chunks of the monolithic BSD kernel embedded).
http://en.wikipedia.org/wiki/Darwin_(operating_system)#Kerne...
Concerning the BSD portions, see this from Apple's Kernel docs: http://goo.gl/1sp69
"Integrated with Darwin is a customized version of the Berkeley Software Distribution (BSD) operating system. Darwin’s implementation of BSD includes much of the POSIX API, which higher-level apps can also use to implement basic app features. BSD serves as the basis for the file systems and networking facilities of OS X. In addition, it provides several programming interfaces and services, including: The process model (process IDs, signals, and so on); Basic security policies such as file permissions and user and group IDs; Threading support (POSIX threads); Networking support (BSD sockets)"
That accounts for an immense amount of what a kernel normally does.
Besides, I have never met a NeXT or Apple employee that didn't consider Darwin to be BSD.
It's a radically modified BSD but I think it's still a descendant.
Not exposed to standard users, no.
There's no relationship between the existing projects and the Free/OpenBSD open source work.
That's simply not true. There's more to the BSDs than just the kernel – all of the userland stuff is incredibly important to Apple, especially as they try to further distance themselves from the GPL. There is a relatively strong relationship between the BSDs and OS X/iOS. It's true, the lower you get, the bigger the differences, but even xnu has some relatively current BSD sources. e.g. from OpenBSD:
http://opensource.apple.com/source/xnu/xnu-2050.7.9/bsd/net/...
I, and some other developers I know, have been hoping that Apple in the future will sync with FreeBSD again in the future, hopefully against FreeBSD 10 to get even more feature parity in kernel interfaces available.
There is a lot of a relationship between Darwin and the FreeBSD team. Apple's firewall import from OpenBSD (pf) for example was also used by the FreeBSD team to update their port.
Just because it is not visible on the surface doesn't mean the relationship doesn't exist ...
There was OpenDarwin though, which the developers shut down due to lack of interest and other problems. Now there's PureDarwin but development seems very slow.
Clang/LLVM (which has substantial support from Apple) will be the primary compiler for FreeBSD.
Apple's Grand Central Dispatch (libdispatch) has been ported to FreeBSD.
http://en.wikipedia.org/wiki/Grand_Central_Dispatch
The TrustedBSD Security Event Auditing and OpenBSM are based on the Mac OS X BSM audit implementation and donated by Apple.
As well, CUPS has been ported to FreeBSD.
Well CUPS did not originate with Apple, they bought it when they needed a mature printing system. It existed for BSD prior to Apple's purchase.
I don't know if the BSD's have made any use of anything from Apple's Darwin release? Perhaps it's not possible due to the licencing (Apple Public Source Licence) which is copyleft'ish.
As others have mentioned, stuff like the TrustedBSD and Audit framework came from Darwin, and features such as Seatbelt and sandboxes are slowly being considered or improved upon by Capsicum for example.
But outside of developers and hackers, most people have so little exposure to the Unix side of MacOS X (and practically none on iOS) that it wasn't as big an impact as some of us (unrealistically?) hoped.