Misinformation is false information that’s given without malice, and disinformation is false information, such as government propaganda, that’s given with the intention to deceive.
The “mis-“ prefix and the “dis-“ prefix can both negate things in a lot of ways, and they have taken on different meanings in “misinformation” and “disinformation.”
The "mis-" prefix can mean “wrong,” “mistaken,” “badly,” or just negate the meaning that follows. Misinformation is information that is incorrect, but the word is meant to carry a connotation that the bad advice was given without malice. Here’s an example from the novel “Jonathan Strange & Mr. Norrell":
“Besides,” said Mr Norrell, “I really have no desire to write reviews of other people's books. Modern publications upon magic are the most pernicious things in the world, full of misinformation and wrong opinions.”
And another example in advice from the Irish writer William Trevor:
“I have never believed in the axiom that a writer should first and foremost write about what he knows. I think it’s a piece of misinformation.”
Another example of a word that uses the “mis-” prefix to describe an unintentional error is "misspeak."
I was surprised to learn that "disinformation" came to English from the Russian word "dezinformatsiya" and refers to false information that is deliberately intended to mislead, especially when it is distributed to other countries.
Here’s an example from Ben Goldacre’s book “Bad Science”:
"Carrots were the source of one of the great disinformation coups of World War II.”
Yes, carrots. And this story sounded too good to be true, but I looked it up and “Smithsonian Magazine” and Snopes both have it too. Apparently, the British Royal Air Force was using a new type of radar in 1939, but they wanted to keep it secret, and the Germans were noticing that British pilots were suddenly really good at detecting their planes in the dark as they tried to cross the English Channel.