What gun is known as a Saturday Night Special, and why?

No single gun but a catogory of guns.

"The phrase Saturday night special (SNS) is a colloquial term used in the United States and Canada for any inexpensive handgun, especially a mousegun/pocket pistol."

https://en.wikipedia.org/wiki/Saturday_night_special

Any inexpensive Gun that can be purchased, used on a "Saturday Night" (the common night for trouble) then thrown away.

Saturday night special is a pejorative or slang term used in the United States for any inexpensive handgun. It is sometimes called an SNS in written shorthand. Traditionally, Saturday night specials have often been defined in some legal jurisdictions as compact, inexpensive handguns with a barrel length of under three inches (for pistols, overall length of under six inches) and low perceived quality, although there is no universal official definition of "Saturday night special" under any federal or state law [1] [2]. The weapons' low cost and availability make them attractive to low-income buyers despite their shortcomings.

The term junk gun is commonly used for the same class of inexpensive handguns; many state and local laws aimed at regulating inexpensive guns use this term. Other terms used for small handguns that do not reflect negatively on quality or expected use are pocket pistol and mousegun.

https://military.wikia.org/wiki/Saturday_night_special