Are Darius King of Persia and Cyrus King of Persia the same person

No. Cyrus the Great was the Persian king who defeated the Babylonians and allowed the captive Jews (and other ethnic groups) to return to their homelands. Cambyses succeeded after the death of Cyrus, then Bardia (or Smerdis) usurped the throne while Cambyses was in the provinces, coincidently shortly before his death. Darius overthrew Bardia and ruled as king. The confusion between Cyrus and Darius arises because the Book of Daniel, believed to have been written in the second century BCE, incorrectly attributed the defeat of the Babylonians and the freeing of the Jews to Darius. The bible clearly shows that Cyrus and Darius are different and shows that Cyrus was the one who released the Jews but because of the opposition, years later Darius had to search for the memorandum that Cyrus had written and order that the work be continued as it had stopped due to opposition from the surrounding people. Ezra6:1