Here's a mnemonic device to start you off: A "bench warrant" usually means someone didn't have their backside on the bench when they should have. That's the bench in front of the judge, not the park bench where pigeons can be fed.

Speaking more technically, a bench warrant is issued by a judge when a defendant violates the rules of the court. Most often, the defendant has simply failed to show up. Once a bench warrant is issued, however, the police can treat it like any other arrest warrant -- and use it to bring the defendant back in front of the judge.

By contrast, the arrest warrant process is started by a police officer. The officer files a statement with the judge explaining why he believes that the person named has committed a crime (in legalese, the officer is showing "probable cause" to arrest the person). If the judge is convinced, she signs the warrant, and the police can make the arrest. That doesn't mean that police officers must go running back to court for arrest warrants for every purse-snatcher they see. Many arrests do not require a warrant at all. The most typical use of an arrest warrant is when an officer wants to nab an unsuspecting suspect in the comfort of his or her own home. Simply busting down the suspect's front door in such a non-emergency situation would be neither polite nor legal.