Command-line-wise, almost none, although this has been changing (for better or worse). Linux has a much larger market appeal and following than any commercial UNIX. GUI-wise there are also no major differences--Linux, as most other UNIXes, uses an X-Windowing system.
The major differences:
Linux is free, while many UNICES (this is supposed to be the plural of UNIX), are very expensive. The same for applications--many good applications are available on Linux free. Even the same commercial application (if you wanted to buy one) typically costs much more for a commercial UNIX than for Linux.
Linux runs on many hardware platforms, the commodity Intel-x86/IBM-spec personal computers being the most prominent. In contrast, a typical UNIX is proprietary-hardware-bonded (and this hardware tends to be much more expensive than a typical PC clone).
With Linux, you are in charge of your computer, whereas on most UNICES you are typically confined to be an "l-user" (some administrators pronounce it "loser").
Linux feels very much like DOS/Win in the late 80s/90s, but is much sturdier and richer, while a typical UNIX account feels like a mainframe from the 60s/70s.
Some UNICES may be more mature in certain areas (for example, security, some engineering applications, better support of cutting-edge hardware). Linux is more for the average Joe who wants to run his own server or engineering workstation.