I know what you are getting at. YES the equations are the same, but NO they are not the same. I doubt you need to know the specifics but here are some basics that might be helpful. Closed at both end are like in string instruments, open at both ends are in types of wind instruments. Closed have a node at each end, open have an antinode at each end. Besides this I don't think there is much else to know in terms of differences.