In Texas, there are three major types of warrants a judge or magistrate may issue. A warrant can only be issued by a judge or magistrate -- the prosecution cannot authorize a warrant on their own for your arrest, but they can recommend to the judge.
An Arrest Warrant is a warrant that authorizes law enforcement to arrest an individual. An arrest warrant can be used to arrest anywhere they find that individual. A judge must agree there is probable cause in order to sign off on an arrest warrant.
A search warrant is a warrant that authorizes law enforcement to search in a particular place for a particular thing or items. The warrant must outline the areas to be searched and what is sought. A judge must agree there is probable cause in order to sign off on a Search Warrant.
Lastly, when a defendant in a criminal proceeding fails to show up for a scheduled court date -- one that he or she was ordered to appear at -- a judge may sign and issue a bench warrant. A Bench warrant is an arrest warrant issued by the judge during a criminal proceeding, without suggestion or application from law enforcement. It has the same effect as an arrest warrant; it just is authorized in a different way.