Most police records at least in the U.S. will show arrests. Once arrested it is up to the District Attorney to determine if will be "charged". Usually on first offense there might be a diversion program and there is no conviction. However, the initial arrest would probably still show up on a police report.
On many employment application, the question is if you have ever been arrested. This includes arrests not charged. Even if a record is "expunged" the arrest will still show up. And immigration usually has the most detailed records available from the home country,