A mask is called a persona in theater. This, in turn, came to mean the social face people show to the world. Char always wears a mask. He took his physical mask after the "One Year War", but kept his psychological mask on.
He was always playing a role. Maybe, in the process, he forgot who he truly was.
Initially, he wore a mask for obvious reasons. He was the orphaned son of the father of the Principality of Zeon, Zeon Zum Deikun, and was secretly plotting to avenge his presumably assassinated parents, by taking revenge on the Zabi family, who are now in control of Zeon.
So is his true face under his mask, a man of revenge? Not quite. He tricked the youngest Zabi, Garma, into getting killed by Gundam, but he didn't get any satisfaction, and instead, felt empty. It's difficult to judge if he was speaking from his heart, but his actions shifted away from taking revenge on the Zabi family, so he probably felt that a man of revenge was not his true color.
Also, when he reunites with his sister, Sayla, in "Mobile Suit Gundam" Episode 38, he asks her, "Do you think I'm just a man of revenge?" It's as if he is trying to tell her that his actions are for a greater cause. Later, he actually does try to free "those whose souls are drawn by the gravity of Earth" and achieve human innovation by making all humans live in space.
Then is a revolutionary his essence? That also doesn't quite fit him, because he calls himself a "clown" when he makes these revolutionary speeches.
His idea of human innovation must be inherited from his father, Zeon Zum Deikun. Does this mean he is following the steps of his father, who passed away when he was still young? However, the story hints at his mother's death having a stronger impact on him than his father's.
Char's past was shown in "Mobile Suit Gundam: The Origin", and it describes him being more shocked by learning his mother's death more than his father's. Moreover, he has always sought for a woman with motherly traits. His lines in "Mobile Suit Gundam: Char's Counterattack", "Lalah was the one who could have been my mother," is symbolic.
To him, a revolutionary was just another mask.
He even has several names he goes by. Char Aznable, his given name Casval Rem Deikun, Édouard Mass, and Quattro Vageena. And it's not only his name that changes. His social status and rank have been all over too. He was both enemy and ally to Amuro. Char's life is full of twists and turns. This is a stark contrast to Amuro, who was always a Mobile Suit Pilot.
Char never was able to become who he wanted to be. First, he failed to be a man of revenge. He also couldn't become a revolutionary, nor a cold dictator, and was only a "clown". Gihren Zabi was a better dictator than he was. He probably didn't think of himself as a clown and was gloating over his own political speeches.
Most importantly, Char failed to become a true New Type, and that's what makes him different from Lalah and Amuro. He probably asked himself why he couldn't become a true New Type upon seeing other New Types like Haman, Sirocco, and Kamille. He had an inferiority complex towards Amuro, and how he used people around him as tools made him the Old Type that he despised.
Char wanted human innovation more than anyone, but he couldn't put behind his Old Type ways.
His true face under his mask is an empty "nobody". But that emptiness resonates with us "nobodies".