Since I don't have any philosophy background, please answer as simply as you can! Thank you!
mohammad-ghasemi, welcome to PSE.
A dictionary will tell you that 'untrue' = 'false'. But your question is about conceptual distinctions expressed in ordinary language. A dictionary does not always do justice to such distinctions. Nor is the matter to be settled by saying by the principle of bivalence in logic that there are only two truth values - true and false - so that 'untrue' can only mean 'false'. Ordinary usage is the key here, neither dictionaries nor logical principles. It's a question of how a language community uses language.
I think we use 'false' when we want to assert the contradictory of a true statement or at least of a statement we take to be true. 'I met X last week' (true); 'I did not meet X last week' (false). The sentence 'I met X last week' is at least by ordinary language standards not vague, ambiguous, lacking in a unique meaning. So if it is true, there is a clear contradictory,' I did not meet X last week', which is false.
In contrast we use 'untrue' when e.g. vagueness creeps in. In a familiar example, due to JL Austin, 'France is hexagonal'. I don't want to say simply that this statement is false, because there is a vague sense in which France is hexagonal. So instead of saying, 'It's false that France is hexagonal', I say 'It's untrue that France is hexagonal' - meaning that it is not strictly (geometrically) true that France is hexagonal but not simply (in common sense, everyday terms) false either.
'False' indicates definite, unqualified error; 'untrue' suggests that the statement does not have a unique meaning and cannot be endorsed as it stands. So I might say, 'France is hexagonal' is untrue because it is not geometrically hexagonal but it is approximately hexagonal on the map. 'Untrue' qualifies my rejection; 'false' does not.
In referring to vagueness I have in mind only one way in which the false/ untrue distinction might come into play. This is not a full account; I'm sure other angles are possible.
I went to the market where I ate an apple.
Did I go to the market?
"Yes" = true
"No" = false
"I ate an apple" = untrue
Untrue is equivalent to the expression "that's not even wrong!"