Legal Question in Criminal Law in California

Re: definition

A full answer to your question would require much more space than this web site allows, so I'll try to be succinct instead. Keep in mind that this answer is somewhat imprecise as a result.

An investigative detention is a stop by police officers for the purpose of asking questions. If an average reasonable person under similar circumstances would expect to be allowed to continue on his way after a short time, the stop is merely an investigative detention.

If the circumstances would lead the average reasonable person to believe he would not be free to leave shortly, then the detained person is in custody. For legal purposes, "in custody" is generally the same as "under arrest", though police can decide to release a person in their custody without actually booking him or issuing a citation -- which is what most laypeople would regard as the defining elements of an arrest.

California law and federal law are identical on this subject, because it is governed by the federal constitution. Note that there is only case law in this area and and that there are no applicable statutes. The case law interprets the Fourth Amendment of the U.S. Constitution, and states are obligated to respect the rights granted by that document. They are free to grant additional rights beyond what the U.S. Constitution requires, but California has not done so and I do not believe any other state has, either.