Being an MC is bigger than making rap music for cacs to profit off of. You aren't an MC just because you make rap music or call yourself a rapper. Now a lot of rappers are MC's just by the very nature of rap as an art form because it is speech-craft. What creates distinction between simply rappin and MC'ing is intention and purpose, IMO.
Think of all of your favorite orators outside of rap music...MLK, Malcom X, Richard Pryor, George Carlin...shyt Obama and other presidents that knew how to MOVE THE CROWD, these men are MC's, they have presence, magnetism, vision and purpose with their speech-craft.
If we try and contain this within rap music (something is distinct from Hip Hop as a culture, IMO) then it just becomes about preferences. It can be apart of it because it's an aspect of the ART of rap and thus supports the purpose and intent, but it's not the crux of the issue.
No music, no rhymes, but he's still moving the crowd. Pac woulda been an MC whether even if he had never cut a single record.
So I say If you really want to tell the difference between someone who is an MC and a rapper...remove the music out of the equation and see what you have left. It's not that it's "elitist" to deem rappers of the more poetic or lyrical variety to be MC's, it's just that if I were to turn the music off, is there still something there that is poignant, truthful, artistic or something that isn't strictly self serving being displayed? A lot of "rappers" are just utilizing rap to make money rather than trying to 'move' something, speak for somebody or invest in/elevate the art of rap.