These three men represent three different approaches to civil rights, although some might say that the differences were caused more by when and where the men lived, not necessarily their own attitudes.
Booker T. Washington represents the most accommodationist thinking of the three. Washington lived in the Deep South in the late 1800s. His was the most repressive environment of the three. He believed that African Americans should not be too demanding. He believed that they should stay in their own place in Southern society and work hard and that whites would then grant them rights in due time.
Marcus Garvey lived in New York (during his time in the US) in the late 1910s and the 1920s. He was a black nationalist. Garvey did not believe that blacks should wait for whites to give them rights. In fact, he (like Malcolm X in decades to come) did not believe that blacks should really try to integrate. Instead, he wanted to them to help themselves and create a separate community for themselves. This aspect of self-help only was similar to Washington’s in some ways.
King lived in the Deep South like Washington, but was active in the 1950s and 1960s. He was the most integrationist of the group. He believed that African Americans should demand their rights. However, he believed that they should do so in cooperation with like-minded whites. He was not a nationalist.
Thus, the three men had some similarities, but also held fundamentally different ideas on important matters.