The term fake news has become more complicated as it gets conflated with media bias and other criticisms of mainstream media. Use of the term has become a way to discredit news sources that an individual disagrees with.
"Evaluating news sources is one of the more contentious issues out there. People have their favorite news sources and don't like to be told that their news source is untrustworthy.
For fact-checking, it's helpful to draw a distinction between two activities:
Most newspaper articles are not lists of facts, which means that outfits like The Wall Street Journal and The New York Times do both news gathering and news analysis in stories. What has been lost in the dismissal of the New York Times as liberal and the Wall Street Journal as conservative is that these are primarily biases of the news analysis portion of what they do. To the extent the bias exists, it's in what they choose to cover, to whom they choose to talk, and what they imply in the way they arrange those facts they collect. The news gathering piece is affected by this, but in many ways largely separate, and the reputation for fact checking is largely separate as well."
Some organizations research news organizations and evaluate the general accuracy of their news reporting and their political positions. Among these is Ad Fontes Media. Ad Fontes has created and periodically updates a Media Bias Chart which categorizes news sources on two dimensions--accuracy of their factual and investigative reporting on one dimension and, on a second dimension, their editorial positions on a left to right scale. Ad Fontes also exposes their rating methodology.