Are declarations of heresy limited to the denomination that made them?

Take for example Pelagianism, which was condemned as heresy at the Council of Carthage in 418 (disclaimer: I am not at all inclined to believe Pelagianism or attempting to discuss the specific doctrine, it's just the first example of heresy I thought of). As I understand, the council was Catholic. Does this mean only Catholics necessarily regard Pelagianism as heretical? Do Protestant churches tend to agree with Catholic declarations of heresy, and/or vice versa? Have there been any Protestant declarations of heresy equivalent to the various Councils? I realize that's several questions but they kind of sum to the main question I've asked.