If there is a problem, you need to communicate it.
The question is that is there a difference between the two phrases? If yes, then what is it?
Both of them seem correct. So what is the rule here (in proper/standard English Grammar)?
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There is no requirement to use then in conditional sentences at all.
There has been a lot of work carried out on the meaning of this word in conditionals, but none of it has been very conclusive. Here is a post I wrote for Philosophy Stack Exchange on the subject:
Then is not really a logical connective at all. It is used in conditionals, but it is just an adverbial discourse marker. What it seems to show is that the speaker is prepared to assert what's coming next on the basis of whatever it is that then is referring back to as being the case. It doesn't only occur in conditionals:
Notice that there are no sentences in which the inclusion or omission of the adverb then makes any difference whatsoever to the truth conditions of the sentence. In the Original Poster's question the sentence has exactly the same truth conditions whether or not then is omitted:
The fact that adding or omitting then can never change our assessment of whether a conditional sentence was true, is evidence of the fact that it is not actually a logical connective. It merely adds a higher order comment about the speaker's attitude to a proposition.
Probably the best known work on the use of then in conditionals is by Sabine Iatridou On the contribution of conditional THEN. However, readers beware, the grammaticality judgements therein are, in my opinion, rather suspect in several places.
Iatridou pointed out that we are most likely to use then when we would not expect Q to happen unless P. There are many other interesting observations as well.
In short, however, then is not a logical connective at all.
I would argue that the use of then in if-then clauses offers clarity and makes the structure easier to understand. It says that the speaker is done defining the conditions and is now going to present the consequence of the conditions.
Obviously, some expressions are less complex than others, so it is less helpful for simple statements.