My understanding - Lashon Hara is gossip about the truth; Motzi Shem Ra is slander - based on false assumption.
Let's say that someone saw me go into a non-kosher restaurant. All I did was use the restroom. That person tells others what I did and the gossip spreads. He tells others that he saw me go into a non-kosher restaurant, and leaves it at that. That's lashon hara.
If that same person says further that I ate a cheeseburger there, that's motzi shem ra.
My question - in all these examples, am I not allowed to enter these places because of marit ayin because someone MIGHT dispense lashon hara / motzi shem ra about me? Do I have any obligation to prevent another Jew from doing something wrong himself even when in the last example, I'm not doing anything wrong at all, but an observer may think that I am? Do I have to prevent possible lashon hara and is mar'it ayin any form of such prevention of lashon hara?