Opinions / Beliefs with Tikkun Olam and Moschiach?

Hi! I’m a newbie and one of the things I have seen frequently is the Tikkun Olam or Messianic Age to come. Some sects denounce the idea of a Moshiach while positing that it is up to the Jewish people to usher in the Messianic Age by promoting justice, etc. Some sects uphold the belief that a Moshiach from the Davidic line will come and fulfill the prophecies. Some even hold that the Lubavitcher Rebbe is the “King Moshiach.”

Where do these differences in interpretation come from? Why do Reform synagogues denounce a Moshiach figure? Why do some Chasidic synagogues believe the Lubavitcher Rebbe is King Moshiach?

Thanks!