No, "fake news" refers to a very specific phenomenon. It's not just any kind of misleading or incorrect reporting. Trump was the one to start saying "not fake news, YOU'RE fake news", but the phenomenon as initially encountered was about shoddy and small fraudulent websites, often trying to deceive their audience to believe that they were a different website, pushing the most anger-inducing news. It wasn't about left vs right (and why are those the only two options, argh).
It's a far cry from the NYT or Fox News reporting incorrect things, whether deliberately or not, to someone called Foxx News or Non York Times reporting that Islam causes prostate cancer.
If you look at the list here, it's all over the political spectrum, some of it is just plain apolitical scams like the Hawking Scam on a CNN knockoff website or celebrity stalking:
https://en.wikipedia.org/wiki/List_of_fake_news_websites#Lis...