The police stopped you. Were you arrested? Detained? Did they have probable cause? What about reasonable suspicion? Read here for all kinds of information about the rules regarding apprehension of suspects.
Arrest Warrants: What's in Them, How Police Get Them
Police must convince a neutral judge that, more likely than not, a crime has been committed and the subject of the warrant was involved.
What Is an Arrest?
Whether a person is "under arrest" depends on the circumstances of the police encounter.
When the Police Can Make an Arrest: Probable Cause
"Probable cause" requires more than a mere suspicion that a suspect committed a crime, but not as much information as would be required to prove a suspect guilty beyond a reasonable doubt.