Let me add two more things
Every airline and airport are different, but here is the "standard" procedure
You do NOT stay in "international space" since ATH to JTR is a domestic Schengen flight. Both your arrival and departure areas are "airside" i.e. behind security but they are not necessarily connected.
For more details see https://en.aegeanair.com/travel-information/at-the-airport/connecting-passengers/ and click on "Extra Schengen – Intra Schengen"
Credit:stackoverflow.com‘