1: Fact/Matter of fact: An observable phenomenon that can be independently verified. Facts are independent of your knowledge of them, your beliefs, your preferences, and your opinions.
"The Moon revolves around Planet Earth."
"You may die of a CoViD infection."
"The 2021 flooding in Europe was caused by heavy rainfall/a poorly designed flood warning system/poor preparation by town planners/climate change."
In the last example, note the diversity in causes, reflecting the progression from proximate to ultimate causes.
2: Belief: A feeling that something exists or is true. The origin of a belief may stem from a combination of facts, misinformation, disinformation, and or preferences.
"I believe God created the universe."
"I believe CoViD is a hoax."
"I believe climate change is happening."
3: Preference: A favoured choice. The origin of a preference may be known or not -- observation, indoctrination, operant conditioning, delusion. Values are preferences.
"I like chocolate cake. I don't like Black Forest cake."
"I prefer a fixed-rate mortgage over a variable rate, because it gives me greater piece of mind."
"Honesty is important to me. I don't know why."
4: 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.)