This is not an easy question with a simple answer. As I, a non-lawyer, understand it, the authority to "detain" and investigate is explained in a supreme court case : Terry v Ohio. Terry v Ohio and subsequent cases say that in order to detain and investigate someone, a law enforcement person needs "reasonable, articulable suspicion" of criminal activity. That includes demanding that someone provide identification. A law enforcement person has the authority to initiate a consensual encounter with anyone at any time and ask any question desired, but unless a person is being lawfully detained IAW Terry, no actual response is required. Exceptions exist in traffic infraction cases, and the like, which may be civil or criminal depending on where in the US you are and the nature of the infraction. Also, suspicionless dui/driver's license checkpoints may be permissible, and they actually occur, but some debate whether they are conducted within the constraints of Supreme Court decisions or not. I'm told that some probation/parole requirements dictate that a parolee/probationee must consent to searches and investigations as a condition of release -- I have no experience, but I think that's true.

So, you can probably see where the "am I being detained" thing comes in. If a police officer stops you and asks you for ID, it's not clear whether you are being detained, arrested, or just subject to a consensual encounter. Before continuing with the encounter, whatever its nature, someone may want to clarify the nature of the encounter. If someone is being lawfully detained, it may be necessary to provide identification, though unless there is some other reason, for example, you're driving, no actual physical identification is ever legally required.

Now, the search/frisk thing. In order to conduct an actual search, a higher standard than suspicion is required -- that is, probable cause. It's hard to say, as a lay person, exactly what that means. It's lawyer speak. Also, if someone is being arrested, a search incident to arrest is authorized. This may include searching an impounded vehicle, I'm not sure. A frisk, or pat down, is not an actual search, but just an outside touching so that the officer can be confident that someone doesn't have a weapon. It's not supposed to be used to feel for a baggy of drugs, or a fat wallet full of money -- just for weapons. I'm not sure when someone does and doesn't have the right to refuse a frisk/pat down if they are not being lawfully detained.

All this suspicion/probable cause stuff is not real easy to figure out, but someone asserting a right is not supposed to be used to create suspicion or probable cause. For example, if an officer asks you where you work or where you are going or where you are coming from and you lawfully refuse to answer, that refusal is not supposed to create legally actionable suspicion of criminal activity. Just like taking the fifth is not supposed to be used to infer guilt.