In TGS, ch.15, Rand visits Moridin in his dreams due to their bond. However, Rand states that this place isn't exactly TAR, because "this place felt different from the dream world, and oddly familiar."
It has e.g. light without any lamps and the fire doesn't give heat like in TAR.

It's similar to Moghedien's description in ACoS, ch.25, when she meets Moridin the first time:
"She did not doubt it was somewhere close by Shayol Ghul, though; it did not have the feel of Tel'aran'rhiod, the only other possibility."

IMO, this place is a corrupted part of TAR near SG, where the bubbles of evil orginate to be sent into the Westlands.

It's interesting to note that Moridin's place contains most of the signs of a twisted, chaotic reality, we also see in the Westlands in TGS:

Rand mentions that "he chose one of the doors at random — he knew that it wouldn't matter which one he picked" and enters Moridin's chamber. That fits with the changing of places corridors e.g. in the WT.

Moreover, Rand also sees the unnatural clouds/storms and nightmarish visions there, like others did in the Westlands: "They were the clouds of an impending storm, unnatural though they were. He looked more closely, and saw that each new cloud formed the shape of a tormented face, the mouth open in a silent scream. The cloud would swell, expanding upon itself, face distorting, jaw working, cheeks twisting, eyes bulging. Then it would split, other faces swelling out of its surface, yelling and seething."

The stones in the chamber seem melted, like we saw Leane's cell melting like wax: "The stones that formed floor, hearth and columns were warped, as if they had been melted by an extreme heat. At the edges of his vision, they seemed to shift and change. The angles and proportions of the room were wrong."

There is also vermin mentioned, namely unnatural rats crawling behind the walls.

Rand mentions that "something was different this time, however. Something about the colors. Many of the stones were black, as if they'd been burned, and cracks laced them. Distant red light glowed from within, as if they had cores of molten lava."

Apparently a sign of the DO becoming even stronger. It's also interesting that Rand can't use his links to the other two ta'veren in this place and that the True Source is far away. This suggests that Rand also won't see the colors, when he confronts the DO in the Pit of Doom and might be blocked from the True Source.

On a related note, we see that the DO is also starting to get more influence on TAR itself in TGS. Perrin mentions that in TAR now "the sky was stormy. Normally, clouds in this place were as transitory as other things. It could be completely overcast; then, in a blink, it would suddenly be clear. This time, those dark storm clouds remained. They boiled, spun, and shot lines of lightning between different thunderheads. Yet the lightning never struck the ground, and it made no noise."

Egwene notes similar differences in TAR namely that "she stood in the middle of a small camp, fire smoldering in a firepit before her, a tiny tongue of smoke curling toward the sky. That was odd. Fire was usually too fleeting to reflect in Tel'aran'rhiod. There were no actual flames, despite the smoke and the orange glow warming the smooth riverstones that ringed the pit. She glanced upward, toward the too-dark, stormy sky. That silent storm was another irregularity for the World of Dreams, though it had become so common lately that she hardly noticed it anymore."

It seems TAR in general seems to become like the corrupted part of TAR near SG: in a way more real, but nightmarish. If the DO starts to corrupt more of TAR now, this might in turn lead to more bubbles of evil.