What's the difference between "gravitas" and "mien"?

What's the difference between "gravitas" and "mien"? I've done some sleuthing on some online dictionaries to make sense of these words, but I fail to see the difference. Take CAMBRIDGE DICTIONARY, for example:GRAVITAS:Definition: seriousness and importance of manner, causing feelings of respect and trust in others (my interpretation: you respect them because they seem serious and intelligent.)MIEN: Definition: general appearance and manner, especially the expression on their face, which shows what they are feeling or thinking EXAMPLES: GRAVITAS:1) He is pale, dark, and authoritative, with the gravitas you might expect of a Booker prize winner2) He's an effective enough politician but somehow he lacks the statesmanlike gravitas of a world leaderMIEN:1) His aristocratic mien and expensive clothes singled him out.2) We should look her in the face with friendly mien, but with posture erect and head held high.In each of these examples, "gravitas" and "mien" seem to convey a shared sense of "one's attitude, behavior, and manners they put on when in public"