As your Wikipedia quote notes, Erebos is the personification of darkness. He is neither a deity nor a domain; he is both. Which aspect of him we are talking about, depends on context.
This is a common pattern for primordials:
- Chaos is the personification of the void, but also the void itself.
- Ouranos is the personification of the sky, but also the sky itself.
- Gaia is the personification of the earth, but also the earth itself.
However, it should be noted that some writers used Erebos as an alternative name for Tartaros, and vice versa. One such instance can be found in The Eumenides, the final play of Aeschylus' Oresteia:
These hoary ancient maidens, with whom never
Hath any god mingled, nor man, nor beast.
Evil was cause of their creation, evil
The murky pit of Tartarus where they dwell
Abhorred by men and by the Olympian gods.
Source: Oresteia, Aeschylus, translated by R.C. Trevelyan
Hesiod - on the other hand - considers Erebos and Tartaros distinct (emphasis mine):
Hail, children of Zeus! Grant lovely song and celebrate the holy race of the deathless gods who are for ever, those that were born of Earth and starry Heaven and gloomy Night and them that briny Sea did rear. Tell how at the first gods and earth came to be, and rivers, and the boundless sea with its raging swell, and the gleaming stars, and the wide heaven above, and the gods who were born of them, givers of good things, and how they divided their wealth, and how they shared their honors amongst them, and also how at the first they took many-folded Olympus.
These things declare to me from the beginning, you Muses who dwell in the house of Olympus, and tell me which of them first came to be. In truth at first Chaos came to be, but next wide-bosomed Earth, the ever-sure foundation of all1the deathless ones who hold the peaks of snowy Olympus, and dim Tartarus in the depth of the wide-pathed Earth, and Eros (Love), fairest among the deathless gods, who unnerves the limbs and overcomes the mind and wise counsels of all gods and all men within them.
From Chaos came forth Erebus and black Night; but of Night were born Aether and Day, whom she conceived and bore from union in love with Erebus. And Earth first bore starry Heaven, equal to herself, to cover her on every side, and to be an ever-sure abiding-place for the blessed gods. And she brought forth long hills, graceful haunts of the goddess Nymphs who dwell amongst the glens of the hills. She bore also the fruitless deep with his raging swell, Pontus, without sweet union of love. But afterwards she lay with Heaven and bore deep-swirling Oceanus, Coeus and Crius and Hyperion and Iapetus, Theia and Rhea, Themis and Mnemosyne and gold-crowned Phoebe and lovely Tethys. After them was born Cronos the wily, youngest and most terrible of her children, and he hated his lusty sire.
Source: Theogony, Hesiod, lines 104-138
The same is true for Aristophanes, no less than two centuries after Hesiod:
At the beginning there was only Chaos, Night, dark Erebus, and deep Tartarus. Earth, the air and heaven had no existence. Firstly, blackwinged Night laid a germless egg in the bosom of the infinite deeps of Erebus, and from this, after the revolution of long ages, sprang the graceful Eros with his glittering golden wings, swift as the whirlwinds of the tempest. He mated in deep Tartarus with dark Chaos, winged like himself, and thus hatched forth our race, which was the first to see the light.
Source: Birds, Aristophanes, lines 690-695