Both the March on Washington and the Birmingham campaign of 1963 were mass demonstrations for civil rights. They were both intended to gain national attention for the cause, and they were both explicitly non-violent. But the Birmingham campaign was more of a direct action against segregation, and was undertaken with the expectation that area authorities would react with violence. The March on Washington was approved beforehand by Washington authorities, including the Kennedy Administration, which actually persuaded the marchers to tone down radical aspects of their message. (It should be noted, however, that Martin Luther King did not organize the march, A. Phillip Randolph and Bayard Rustin did.) However, both events generated memorable documents of the civil rights movement. King's "I Have a Dream" speech and his "Letter from a Birmingham Jail," became synonymous with the aims and philosophy of the civil rights movement, and a major part of its legacy. 

What are the similarities between the Birmingham campaign and the Montgomery Bus Boycott?

Both campaigns involved Martin Luther King's leadership. He emerged as a leader in the bus boycotts, and was asked to come organize the Birmingham campaign by Fred Shuttlesworth. Both were based on non-violent resistance to Jim Crow, though the boycotts involved less direct civil disobedience. Both were received with violence by some area whites. King's house was firebombed in Montgomery, along with many other acts of violence, and the brutality of the police against peaceful marchers in Birmingham has become a notorious symbol of white resistance to the civil rights movement. Both received national attention, which was certainly the goal of the Birmingham organizers, in particular.