The 14th amendment and the Civil Rights Act are very similar in the sense that they are trying to provide equal protection for American citizens.
The 14th amendment states that all American citizens are entitled to the rights outlined in the US Constitution. This would include freedoms like the freedom of speech, religion, press, right to an attorney, right to a public and speedy trial, etc. However, after the Civil War, some southern states would implement state laws that restricted African-Americans from having these rights.
The Civil Rights Act of 1964 also aims to protect American citizens. This focuses on eliminating public discrimination (segregation) and discrimination through employment. This ensures that businesses can't discriminate potential workers based on gender, race, or nation or origin.