Apple losing their server division, and their huge focus on iOS has led to many of their core OS technologies lagging behind. Examples are networking, filesystems (still HFS+), kernel level benchmarks, concurrency, NUMA etc, and especially so compared to what Linux, Solaris, *BSD, and NT have progressed in the last few years. A few years ago, I remember some of their kernel engineers saying Apple's performance goals…
They're known to use "Teradata" (i.e. Dell), "Oracle" (i.e. FKA Sun) & HP DL-series servers alongside NetApp storage. iTunes is reportedly one of the world's largest SAP installations and that'll almost certainly be on AIX or Solaris with Oracle databases on the aforementioned NetApp spindles. OS for other applications? Nothing stops Apple running OSX if they do the driver work, but honestly I'd walk in expecting a mix of Solaris, RHEL and Windows, like every other Enterprise(TM).
[ it'd be nice to think they run a lot of FreeBSD given their UNIX group's credentials but - correct me if I'm out of date here - the bge(4) issues of FreeBSD on HP Gen8 servers seem to undermine that ]
Separately, iCloud is reportedly running on Azure & AWS.
I think it's a pity that Apple abandoned the server market so completely, but I understand how a consumer-first strategy with a strong theme of "same experience everywhere" is antithetical to enterprise needs (specifically the demands of experience control & functional lockdown expected by corporate IT departments). I've done some hard yards inside large enterprises and seen first-hand just how wedded many CIOs are to the whole colossal Microsoft ecosystem; competing with that head-on would be a very long game.