As an average adventuring Imperial citizen, I've always imagined
the Imperial Core as the cultural and bureaucratic center of the
Imperium. Notwithstanding war zones, it is more "civilized" with
higher tech, pop, and law levels than the "frontier" areas such as
the Spinward Marches and other zones adjacent to alien sectors.
It is more a mental image than one born of demographic data.
This reflects the historical mindsets of the Imperial culture, since
the Spinward Marches technically have been populated by Imperials for
around a thousand years, with little expansionist settlement recently
(apart from District 268).
Now aliens would have a different perspective on the Imperium.
Generally speaking, the Aslan treat the Imperium as a frontier ripe
for settlement. The Zhodani see the Imperium as nothing more than a
military threat from backwards thinking people. Human and yet
uninterested in Imperial culture, the Zhodani are exploring in
directions other than the Imperium. I would guess that the space
toward the Galactic Core is unpopulated and ripe for exploration.
I've always heard "Zhodani" used with "core expeditions" to delineate
their perspective, toward the Galactic center, since they are not
interested in Imperial culture.
And if you don't like this explanation, then do away with one of
the Cores, say the Imperial Core, and make another game! 8-O
Keith Thoms