Fact/A matter of fact: An observable phenomenon that can be independently verified.
"Water boils at 100 degrees Celsius."
"Marie Curie was awarded her second Nobel Prize in 1911."
Belief: A phenomenon that is assumed to be true. The origin of a belief may stem from a combination of facts, misinformation, and/or disinformation.
"I believe climate change is happening."
"I believe God created the universe in six days."
Preference: A favoured choice. Values are preferences. The origin of a preference may be known or not -- observation, indoctrination, operant conditioning, delusion.
"I prefer a fixed-rate mortgage over a variable rate, because it gives me greater piece of mind."
"I like chocolate cake. I don't like cheesecake. I don't know why."
"Honesty is important to me."
Opinion: A judgement based on beliefs and preferences.
"In my opinion A Moveable Feast is the best book ever written."
"Socialism is superior to both Communism and Capitalism."
"In order to reduce greenhouse gas emissions, the government should tax gasoline."
(In my life I have learned three things: First, people do not like to stick to facts, they like to stick to whatever it is they believe. Second, people judge and choose even if they know nothing or only parts of the story. And last, people have two standards, one which they apply to themselves, family, and friends, and another that they apply to everybody else.)