The 13th Amendment officially abolishes and continues to prohibit slavery in the US. The 14th Amendment declares all persons born or naturalized in the US American citizens including African Americans.
The 13th Amendment was passed on Senate April 8th 1864. The 14th Amendment was ratified July 9th 1868.
The main difference between both Amendments is that the 14th Amendment considers ex slave citizens, which the 13th Amendment does not do. This means that ex-slaves and African Americans hold rights of citizenship, things that the abolishment of slavery did not give them.
This is why the 14th Amendment was very contested by Southern States, because of that many decisions were held by the US Supreme Court.
