So someone can be a senior level skater in their own country but b/c of age restrictions be junior on the international level.
Yup.
Or they may compete senior domestically and junior internationally even at age 15-18 when they're eligible for both, because they or their federation believes it makes more sense for them strategically to do junior than senior internationals.
I know that the Olympics has age requirements as well.
The age restrictions for the Olympics are the same as for ISU senior championships. (15 as of the previous July 1)