From your description it does sound like detention and not an arrest. But, you can be arrested and then let go without going to "jail," police station etc. Usually you end up with a criminal citation that you'll have to answer for at some point. Another option on minor misdemeanors is for the cop to the release you, and file the charges against you. I see this sometimes on minor charges that need medical treatment so the officer does not have to the hospital with the arrestees. Think a shoplifter that has chest pain after the cuffs are applied. If they have positive ID (license etc.) They can basically "unarrest" and then charge later.
All of these scenarios should lead to some court appearance later (though it could be handled by attorney in your absence in certain circumstances).
It's not uncommon to see an investigative detention with cuffs, then release you to parents and forward report to detectives/local prosecutor to decide on charges.
But, I'm not a lawyer. If a minor arrest like that could cause you issues, say on a background check, I'd consult a lawyer. If not sure, and you have to answer quickly I'd disclose it with explanation that you're not sure.
Even highly stringent background checks know people aren't perfect, but are more interested in total honesty. Theory being if you've already disclosed it to work, it can't be used to blackmail you later. If you hide it, it could and also starts you off with trust issues with work.