She actually belongs to both.
Just as in Babylonia, so in Assyria, there were various Ishtars, or rather various places where the goddess was worshipped as the guardian spirit, but her role in the north is so peculiar that all further consideration of it must be postponed until we come to consider, in due time, the Assyrian pantheon.

There will be occasion, too, when treating of the Gilgamesh epic, to dwell still further on some of her traits.

All that need be said here is to emphasize the fact that the popularity of the Babylonian Ishtar in Assyria, as manifested by Esarhaddon's zeal in restoring her temple at Uruk, and Ashurbanabal's restoration of Nana's statue (_c._ 635 B.C.) which had been captured by the Elamites 1635 years before Ashurbanabal's reign, is largely due to the effected identity with the goddess who, for the Assyrians, was regarded chiefly as the goddess of war and strife.

In worshipping the southern Ishtars, the Assyrian kings felt themselves to be showing their allegiance to the same deity to whom, next to Ashur, most of their supplications were addressed, and of whom as warriors they stood in dread.
Nina.
A goddess who, while sharing the fate of her sister goddesses in being overshadowed by Ishtar, yet merits a special treatment, is one whose name is plausibly conjectured to be read Nina.

The compound ideogram expressing the deity signifies 'house of the fish.' The word 'house' in Semitic parlance is figuratively extended to convey the idea of 'possessing or harboring.' Applied to a settlement, the ideogram would be the equivalent of our 'Fishtown.' It is with this same ideogram that the famous capitol of Assyria, Nineveh, is written in the cuneiform texts, and since the phonetic reading for the city, Ni-na-a, also occurs, it is only legitimate to conclude that the latter is the correct reading for the deity as well.