No. Linux versions all share the kernel as their common ties. Commercial Unix (or just "other" Unices) are usually quite different in the guts of things (like the kernel - an HP-UX kernel wouldn't work on a Solaris system, for example), but their interface may be very very similar.
For a huge list of Unix variants, check out:
http://www.ugu.com/sui/ugu/show?ugu.flavors
The most common, though, (IMO) are Solaris, BSD, Linux, AIX, SCO (now Caldera), HP-UX, and possibly Digital... But like the list above shows, there are / have been plenty to choose from.