There is no big difference between Me too and Time's up. The two words were used as a hashtag to create movements targeted at drawing people's attention to the issue of sexual harassment and assaults against women. Me too is a movement against sexual harassment and it is reported to have been for years. The movement went viral in 2011 after an American actress used Me too as a hashtag on social media.
The idea behind it was that if every victim of sexual harassment could post such on the social media, it would pass a serious message to the general public about the increasing rate of sexual assaults against women. However, following the global attention the Metoo movement drew, the Time's up movement also started in 2018 by Hollywood celebrities as a movement against sexual harassment and violence. Due to the global attention it gained, the movement has been able to raise over $20 million for its legal defense fund to help those who cannot afford the huge legal bills to get justice for a victim. The movement has been able to reach out to over 200 lawyers who volunteered themselves to support the movement.