What is a Miranda and Terry stop?
Terry v. Ohio, 392 U.S. 1 (1968), was a decision by the United States Supreme Court which held that the Fourth Amendment prohibition on unreasonable searches and seizures was not violated when a police officer stopped a suspect on the street and searched him without probable cause to arrest.
The Court held that police may briefly detain a person if they have a reasonable suspicion that the person has committed, is committing, or is about to commit a crime. Because of the important interest in protecting the safety of police officers, police may perform a quick surface search of the person's outer clothing for weapons if they have reasonable suspicion that the person stopped is armed. This reasonable suspicion must be based on “specific and articulable facts” and not merely upon an officer's hunch. This permitted police action has subsequently been referred to in short as a “stop and frisk”, or simply a “Terry stop”. The Terry standard was later extended to temporary detentions of persons in vehicles, known as traffic stops. The rationale behind the Supreme Court decision revolves around the understanding that, as the opinion notes, “the exclusionary rule has its limitations”. The meaning of the rule is to protect persons from unreasonable searches and seizures aimed at gathering evidence, not searches and seizures for other purposes (like prevention of crime or personal protection of police officers).
These days many cops will not even know the difference - especially if they do not work traffic as a usual thing. If you are interested both court decisions are on the net and much has been written about both. Basically if it is a Miranda they need to read you your rights immediately.