The BIG difference is that MLK specifically called for non-violent protesting.
BLM’s stated goals were to destroy things.
RE: BLM to destroy, MLK Jr to be nonviolent.
In the documentary Joan Baez: How Sweet the Sound (2009) American Masters on PBS she said once she was asked by MLK to go down to a southern city to start giving speeches to crowds because he couldn’t make it there for a day. She did. She had talked to him about nonviolence being nearly forgotten in the speeches lately. King hugged her and gave her a kiss on her cheek. She said “That evening in his speech he raised his voice a little a couple of times and paused on “nonviolently”.
I knew that was done for me.”
and Trump called for J6 protestors to peacefully protest