Depends what rights you sold. In the past, I've sold the same story under 1st UK Serial Rights in the UK and 1st North American Serial Rights in the US. (plus other foreign language rights where it sold abroad)
These days more and more publications are looking for 1st English Language Rights, or even 1st Worldwide Rights, so best to check your contract and see what it says.
And remember to always check submission guidelines before you submit to make sure you're happy with the publication's rights requirements.
Willie
Willie