Taken into police custody means being arrested, you will be in the police station until they decide what to do with you, you don't have any freedom. Being detained usually means being physically held back by the police from doing anything or if the state prevents you from doing certain things.

"Custody" has more permanence than "detention". For instance, if the courts grant you custody of a child, you have control of that child as if you were an actual parent. It's not a temporary status. "Detention" refers to restraint. Whether it is temporary or permanent is not specified.