Linux was Linus Torvalds' attempt to create an operating system resembling MINIX. GNU was Richard Stallman's attempt to create an operating system based on the principles of free software.
Linux was missing userspace programs which were provided by GNU, X, and other sources. GNU was missing a kernel and some userspace programs which were provided by Linux, X, and other sources.

Thus, you can have a Linux operating system, a GNU operating system, or a GNU/Linux operating system. The terms are not always interchangeable, but they are all perfectly valid.