Michelle Obama seems to be herself whatever the medium. She seems very down to Earth and approachable. I think that’s not fake, but I can’t be sure.
Melania might be a very real person, it’s just that the person she is is very shallow. She comes across as fake because of the context she’s in and the interests she has in being part of that context. I think she has never had any interest in playing the role of first lady. She doesn’t try much to hide that.
Michelle Obama very much relished the role of first lady and tried to do things to enhance the office. Her personality is warmer and more approachable than the former President’s personality. She wants to be in the mix after her stint as first Lady.
Melania wants to return to cocktail parties, shopping sprees and her friends and family. It’s pretty clear she doesn’t want to be where she is…so, she’s “fake”.