It happens all the time. Officer makes the decision to arrest, puts the person in handcuffs and the car. A supervisor shows up, a story gets changed, or an officer finds out that something proves someone is lying, and the person is released. I've seen it happen when a non-violent offender had warrants, but it turned out they were having a kid's birthday party (discovered when the dad came out to check on the mom because she'd been outside 'smoking' for longer than usual).

Arrested is a step up from detention. Detention = you're not free to leave. Arrested = you are not free to go, you're coming with the officer to jail, and they have belief you committed a crime that you will be charged with (or have a warrant, thus already charged). There is nothing that says once arrested an officer can't take off handcuffs and let you go. There really isn't that much distinguishing the two in the law, except for statutes about identifying yourself (where I live, anyway). My laws use the word custody in far greater amounts than arrest.