A bench warrant is an arrest warrant that comes straight from a judge (presumably sitting on their bench) and is usually due to failure to appear in court over a civil matter such as a ticket, simple traffic case, or a child custody case. It's never okay to skip a scheduled hearing without just cause, and failure to attend will almost always have consequences. The purpose of a bench warrant is to deter defendants from missing their court ordered appointments. A bench warrant is different from an arrest warrant, in the sense that with an arrest warrant law enforcement is actively looking for the person to arrest. This is usually due to more serious matters like robbery, assault, or worse.
After you're arrested for a crime, the next step is the filing of the information or indictment. In most cases in Florida (except Capital) the police will fill out a standard police report (A-Form) that will be passed on to the State Attorney's Office who will review the case and determine what crimes they will formally charge you with.