The Earth's gravity well extends far beyond the atmosphere. The moon is for example is well inside the gravity well and even the hill sphere meaning Earth's gravity is the dominant gravity force on the moon.
From one of my favorite episodes of X-Files, where I first heard the term "inner space," I define it as subterranean/oceanic. The space within our planet. The episode was talking about aliens that came from the center of the Earth, as opposed to space. And I always thought that was a neat twist. It was also one of those weird ass ones Duchovney directed so it was high on the humor scale and featured the Lone Gunmen which I always liked.