Both types of warrants involve a decree or order issued by a judge commanding the sheriff or other law enforcement officer to capture and deliver a person to the Court.  The primary difference between the two is the circumstances surrounding their issuance.  A bench warrant is issued "from the bench" by a magistrate or Judge sitting on a particular criminal case, the usual reason is due to a failure to appear by the defendant on a criminal case. Other reasons can include the failure to comply with orders of the Court such as not providing proof of enrollment in a DUI class or proof of completion of community service. 

An arrest warrant on the other hand is issued after the filing of a criminal complaint alleging criminal charges.  The process works as follows:  The district attorney gets a police report which contains evidence of criminal conduct, the DA reviews the reports and decides to file a case against the accused, the prosecutor then files a formal complaint with the Court and a case number is assigned.  Thereafter a Judge reviews the allegations and orders an arrest warrant to pick up the defendant and bring him or her to Court to answer to the charges.

Both types of warrants can be recalled and quashed with the help of an experienced criminal defense attorney.