For practical reasons, yes.
Probably could use POSIX as an umbrella term for all Unix and Unix-like systems. The Unix separation mainly comes from:
- UNIX being reserved for "genetic UNIX", those commercial systems are based on SysV.
- The BSDites, that have weird things in their rc.d/init.d files and use the fugly /dev/ttyXX everyone else stopped using since the Unix98 PTY spec came out
- The "Unix-like" OSen, of which Linux is the most known. Some purists insist to call this GNU/Linux, and the same purists will go up in flames if anyone were to call Linux "Unix".
In reality, the GNU OS was never finished. Linus built a kernel and put the GNU tools over that, thus the GNU/Linux controversy began as GNU thinks that Linus Torvalds only built the kernel and thus didn't really make a full OS from scratch. Meh.