If you write enough crime stories, you’ll eventually encounter a variety of different references to a kind of plea that stands in the no-man’s-land between guilty and not guilty (note: there is no such thing as a plea of “innocent”).
They go by various names: “no contest,” “nolo contendere,” and the “Alford Plea.” The first and second in this list mean exactly the same thing (nolo contendere is legal Latin). There are some minor technical differences between the first and last, but they are basically the same thing.
In a nutshell, these pleas do not admit guilt, but do admit that the state has enough evidence to convict. Defendants generally accept such a plea as part of a plea bargain, admitting to a lesser charge that will let them avoid the harsher punishment of the original charge.
No contest and Alford pleas differ from ordinary guilty pleas in that they are thought to offer some protection from a civil suit arising out of the crime.
In newswriting, I almost always go with “no contest,” which doesn’t involve Latin or the name of some guy nobody’s ever heard of. However, there are plenty of newsrooms where “Alford plea” is the preferred usage, so it may just be a regional thing.