civil rights concern the basic right to be free from unequal treatment based on certain protected characteristics (race, gender, disability, etc.) in settings such as employment, education, housing, and access to public facilities.
Civil liberties concern basic rights and freedoms that are guaranteed -- either explicitly identified in the Bill of Rights and the Constitution, or interpreted or inferred through the years by legislatures or the courts.
examples for civil liberty
The right to free speech
The right to privacy
The right to remain silent in a police interrogation