The page 7 reference is to the chart at the bottom of the page called “Spaces on the Game Board”. It defines an island group as a game board space. A land territory is also defined as a game board space, so the definition on page 8 of an island as a territory located inside a sea zone also defines it as a separate game board space.
There’s also this FAQ entry:
Can a fighter take part in a naval battle in a sea zone and then in a battle for the island in that sea zone?
No. The island is not part of the sea zone; it’s a different map space that is adjacent to the sea zone but not part of it.