I love cozy mysteries
What is a cozy mystery? Why isn't it just a mystery?
Cozies are, as Tabby Uprising described, a quieter type of mystery. The general formula is you have a small-town protagonist who somehow stumbles across a mystery in each book for various (usually implausible) reasons, who also has some unique hook that readers might relate to. The main character owns a bakery, for example, or plays bunko, or knits, or owns cats, or works at a ski shop, or does DIY home renovations - something hobby-like, usually. The mystery is not always murder - it's often a robbery or something less violent. There's almost never any gore or sex explicitly described, and although the main character may have one (or many) love interests over the course of the series, it's usually not anything serious. The plot includes following the process of solving the mystery, but usually includes major side-plots dealing with other characters doing small-town things like putting on a town play or trying not to lose their shop or whatever. Examples are Miss Marple and The Cat Who [whatever].
Procedural mysteries are the other type, and they often are much grittier and darker. The protagonist is somehow involved in law enforcement (detective, police officer, police psychic, bounty hunter, etc.) and the book primarily follows law enforcement's efforts to catch the criminal. The initial crime is usually murder and is usually shown/described in gory detail. The stories involve more immediate danger, gore, sometimes sex, and more "adult" situations (such as the inner workings of a strip club or a drug ring). Good procedurals try to at least get the details correct about how a case is solved, but there's a wide variety of artistic license from series to series
Examples are Hercule Poirot, CSI, or Law & Order.