A civil rights attorney does civil case arguments like Section 1983 lawsuits against police, city officials, and the lke. A criminal defense attorney defends an alleged criminal against crime charges.
It is possible an attorney has the skills and experience to do both. Make sure to inquire of the attorneys you ask about their experience level.
Civil rights include a large spectrum of areas of the law. The Civil Rights Act of 1964 is one such area of law, as is all claims brought pursuant to section 1983 for violation of your constitutional rights in a civil court. The term Civil Rights Attorney is used to describe this type of attorney. Criminal defense attorneys may use many of the same theories of law, but practice within criminal court.
That being said, there is no specific definition of what a "civil rights attorney" is and many criminal attorneys likely also practice in areas of the law that could be defined as civil rights.
Typically a criminal defense attorney represents or advises a person faced with legal jeopardy of criminal penalties. It is defense and the objective is to get the client out of legal harm. A successful defense will not result in anything but the avoidance of criminal penalties -- no money is recovered for the client.
"Civil rights attorney" can be an elastic term, but it typically refers to legal action on behalf of a client where an affirmative recovery is sought from the government (usually) in the form of money or specific action. Civil rights work is typically offense, and the objective is to recover something of value to the client. If the civil rights case is lost, the client gets nothing, but does not face criminal penalties.
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