Google News reports "about 79,000,000 results" for the term "government shutdown," and everyone on both sides of the aisle seems to agree that what's happening right now is a government shutdown. But there is nothing in federal law referring to a government shutdown. And the ubiquitous use of the phrase to refer to what's happening in Washington right now is lazy and sensational.
The term seems to have first been used in late 1980 with the Civiletti Opinion, in which then-Attorney General Benjamin Civiletti interpreted the Antideficiency Act to mean that without a spending bill, government work could not continue. He followed that up with a second opinion decreeing that essential government services could continue without such a bill—which is at odds with any definition of the word "shutdown" in any context other than this.
It wasn't until 1995 that a government shutdown lasting more than three days happened, and the phrase "government shutdown" hadn't even appeared in a law journal until 1994. But by 1995, the terminology had become so widespread that a memorandum prepared by the Attorney General's Office of Legal Counsel chief Walter Dellinger ripped into it in unusually strong terms (for an intergovernmental memorandum):
[P]rior responses to the threat of or actual lapsed appropriations have been so commonly referred to as cases of "shutting down the government" that this has become a nearly universal shorthand to describe the effect of a lapse in appropriations. It will assist in understanding the true extent of the Act's requirements to realize that this is an entirely inaccurate description.
An actual government shutdown, the memo notes, would "produc[e] incalculable amounts of suffering and loss."