Since the kernel and coreutils are GPL there aren't any sue-happy lawyers waiting to pounce upon CEOs saying "We use Linux", the broad family of Linux kernel based OSes (Debian, RHEL, Ubuntu, etc.) have generally gained the marketing term Linux.
I feel that Solaris missed out on this in a shockingly bad manner. Perhaps ex-Sun/Joyent folks can correct me if they feel I'm wrong, but it seems that the Solaris "family" of operating systems has always been way harder to understand than Linux-based, mostly open-source systems. Do I want illumos, OpenSolaris, or OpenIndiana? Or do I actually want Oracle Solaris? Which is the one that Oracle will not try to sue me for?
So here is a broader lesson for people trying to open source their OS, if there is ever a grand project like Solaris. Make it all open source at once, and use a copyleft license like the GPL. Otherwise you risk this kind of breakdown where there are N different operating systems that are vaguely related to and worked on by the same people, but you can't name them in a coherent manner or rely upon broad similarities.