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What exactly are the differences between "correct" and "right", and their negative counterparts, "incorrect" and "wrong"? While I use "correct" and "right" almost interchangeably, I cannot say the same for "incorrect" and "wrong". Please look at the following examples:

I don't think you are correct on that one.
I don't think you are right on that one.

What you just said is correct.
What you just said is right.

That's correct.
That's right.

You are incorrect. (Is this acceptable?)
You are wrong. (I use this form mostly with friends and acquaintances)

What you just said is incorrect.
What you just said is wrong.

That's incorrect.
That's wrong.

I do think subtle differences exist between the above forms, but I can't figure out what they are. Could you please help me with this? Thanks much!

Also, when would one use "not correct" instead of "incorrect", and "not right" instead of "wrong"? How does it make a difference? Thanks again.
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I'd say that "incorrect" refers to specific rules, such as grammar, calculation etc.... Something incorrect is viewed as such by all people aware of these rules/laws. On the other hand, "wrong" is connected to the feeling of what's right or wrong, and hence more subjective.
But then, the meanings overlapse, you can have a wrong answer in a test, or maybe "wrong" tends to be more used than "incorrect".
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Thanks much, Pieanne!
Although most English speakers use "correct/right" and "incorrect/wrong" interchangeably, it is actually correct to use "correct/incorrect" when referring to factual information and "right/wrong" regarding moral issues. It especially matters in examples like "What you just said is incorrect" and "What you just said is wrong." The former suggests that the speakers disagree about factual information, while the latter suggests that the first speaker made a moral error. The same reasoning applies to the use of "correct" versus "right."

Another EnglishForward user put it this way:

"'Wrong' is traditionally used to mean something is morally good or right - or that judgment is correct or inaccurate. It was used to mean an 'unjust action'. For example, it is used when someone is breaking the law.

'Incorrect' is used to point out something is factually wrong or inaccurate. If something is false it is incorrect. On a business document you would inform the company your address is 'incorrect'.

They may seem similar but their meanings and connotations are different.

Connotation refers to a word's set of attributes that create the word's meaning. They do not have the same attributes."

(from Glacierlily )

Additional food for thought: I wonder if the confusion began in association with the different connotations of the word "true" with has traditionally referred to both factual information and moral questions. (An example of the latter might be: "We seek after the Good, the True, and the Beautiful.") At one point in time, making a factual error could have been considered morally wrong because it reflects poorly on a person's character.