Both Malcolm X and Martin Luther King Jr were civil rights leaders in the 1960s. Both of them wanted to improve the status of black people in the United States. Outside of that, there was very little that was similar about them, especially before Malcolm X went to Mecca late in his life.
The major difference between the two was their attitude towards whites. King was an integrationist. He wanted blacks and whites to work together towards a society in which all races got along together and mixed with one another as equals. By contrast, Malcolm X was a black nationalist. He wanted blacks to keep to themselves. He wanted them to have equal rights and to be economically strong just like King did. But he wanted them to get those rights without white help and he did not think that mingling with whites was a good thing.
So both of them wanted blacks and whites to be equal. But Malcolm X wanted them to remain separate while King wanted them to integrate.
Martin Luther King Jr. and Malcolm X were both civil rights leaders during the 1960s, but had different ideologies on how civil rights should be won. Both men were also deeply religious, but followed different religions and paths.
Martin Luther King Jr. advocated nonviolent protest, which had worked well for Gandhi during the years of Indian independence (India became independent in 1947). By organizing sit-ins, protests, marches, and boycotts, MLK jr. hoped to encourage African-Americans that by peacefully and legally protesting, they could build a country where all races are treated equally. MLK jr. was Christian and used examples from the bible to help support his ideas of working together to become more Christian and closer to God.
Malcolm X took a different approach to civil rights when he was imprisoned for a string of burglaries in Boston. In jail, he embraced Islam and converted. Malcolm X appreciated the egalitarian nature of Islam; regardless of class or color, everyone was equal in Allah's eyes. Because he did not see this happening in America, he took a different approach to civil rights. He believed in getting civil rights by "any means necessary"; to defend yourself, and to fight for equality, Malcolm X believed that anything done to achieve these goals was necessary. This brought civil rights outside of the realm of peaceful, legal, nonviolent resistance. For Malcolm X, some violence may be necessary in order to achieve equality for all.
Martin Luther King and Malcolm X both were champions of the African-American cause and fought for equal rights for this historically oppressed community. They both had the greatest impact on the civil rights movement during the 1960s. There were a number of differences between them, none so significant as their approach to achieve the desired results.
MLK was born in a middle-class Christian family and was well educated, while Malcolm X was born in a poor Muslim family and was hardly schooled. MLK was a proponent of non-violence and wanted blacks and whites to exist and work together. Malcolm X, on the other hand, was a supporter of "by any means necessary". He was thus a supporter of using violence, if need be, to achieve his objectives. He was also distrustful of whites and wanted the blacks to support each other.