What difference has "call it the night" and "call it a night"?
According to the google search the both expressions are correct.
call it the night: 20,800,000 hits
call it a night: 9,150,000 hits
Maybe the meaning are same?
The COCA corpus has 95 results for "call it a night" and only 1 for "call it the night", and that single result is:
..if our language is afflicted by a hole right at its center. Let's call it the night of language, the sleep of language.
You see, the meaning is not the same. In "call it a night" you do not specify the "night" too much, you only wish to say:
What we have on our hands is a completed night, now the only thing left to do is to go to bed.
On the other hand, when you use the you mean a night specific enough to take the definite article. In such a situation, I would think that the "night" has been previously mentioned by you, or I will await some "specifying information" in the sentence. In the COCA example, the author refers to some specific period in time when "language sleeps". The author uses an "of-phrase", and this makes the word "night" more definite.
Stop a particular activity for the rest of the day, as in It's past five o'clock so let's call it a day. Similarly, call it a night means "to stop something for the rest of the night," as in One more hand of bridge and then let's call it a night. The original phrase was call it half a day, first recorded in 1838, which referred to leaving one's place of employment before the work day was over. The first recorded use of call it a day was in 1919, and of call it a night in 1938. (The American Heritage® Dictionary of Idioms by Christine Ammer.)