I'd like to know the difference between 'You are in the wrong' and 'You are wrong'.
And even if they are different in meaning, can I just say 'You are wrong'? Is there much difference?
I have to disagree with the other existing answer. "Wrong" and "in the wrong" are very close in meaning, and in a lot of occasions they can be used interchangeably.
If you look up the idiomatic phrase "in the wrong" in a dictionary, among the definitions you are bound to see "wrong." For instance take a look here:
The Free Dictionary defines "in the wrong" as
wrong; morally or legally incorrect.
I am not in the wrong, you are. No, you are in the wrong.
Merriam Webster defines it as
in the position or situation of being wrong
We had an argument and each of us thinks that the other was in the wrong.
It is really a matter of style and/or sentence structure to go with either one. You might as well say
I am not wrong.
We had an argument and each of us thinks that the other was wrong.
I am wrong (maybe I just said 2 = 2 equals 6): means I made a mistake. I am in the wrong (maybe I just said something bad and untrue about another person): means I have sinned.
We are all wrong some of the time. None of us ever wishes to be in the wrong.