What are the differences between False Consensus Effect and Projection?

This video describes the differences between the False Consensus Effect and the Freudian defense mechanism of Projection.
The False Consensus Effect is an effect where people tend to think that others have the same feelings, thoughts, motive, and values. The False Consensus Effect is not an unconscious process.
Defense mechanisms, as described by Freud, protect the ego from unconscious drives, thoughts, and impulses that are unacceptable to society, like greed, aggression, and sexual desires. Defense mechanisms keep the unacceptable drives out of conscious awareness. Theoretically, if defense mechanisms operate for too long a time, they can lead to psychopathology or mental health symptoms in general.
Projection is when individuals assigns their unconscious urges, beliefs, attitudes, and feelings onto other people.