What is the difference between
He became a star by 1990's.
He had become a star by 1990's.
Is the first sentence correct? If yes, then please tell me the difference between the two.
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First, "the 1990's" is a decade not a specific year, so you need to insert the article in each of your questions, and remove the apostrophes (it is not possessive):
1 - He became a star in the 1990s.
2 - He had become a star in the 1990s.
a - He became a star by the 1990s.
b - He had become a star by the 1990s.
That said, the difference is that in sentences 1/2, "he" became a star during the 1990s, and in sentences a/b, "he" was already a star by the time the 1990s arrived.