The Deragoth, or more technically "Dera'tin'jeragoth" meaning Hounds of Darkness in the Tiste Andii language, were the D'ivers form of Dessimbelackis who made a pact with them to divide his soul into seven.
The Deragoth enslaved mankind's ancestors, the Eres'al, 400,000-500,000 years ago.
Based on the behaviour of the Deragoth and Hounds of Shadow towards each other, it was likely there was a connection between the two. Firstly, the Hounds of Shadow Doan and Ganrod, who traveled into the Gate of Darkness within Dragnipur, traveled across the Jaghut Death Bridge towards the statues wherein resided the remaining Deragoth. It was suspected that the arrival of these two Hounds of Shadow had some significance towards the awakening of the two Deragoth who attacked Onrack and Sha'ik's camp in House of Chains.
Furthermore, the remaining five Deragoth in The Bonehunters, upon being released from their statues, pursued the Hounds of Shadow throughout Seven Cities. This pursuit may have ceased following the events in G'danisban involving Poliel. The Deragoth were not seen in Toll the Hounds, however it is stated that the hounds were aware of creatures pursuing them but found "exquisite pleasure" in being hunted and chose to not turn on their hunters.
That being said, there were significant differences between the Deragoth and Hounds of Shadow that might dispel any simple relationships between the two. As L'oric's travels through memory-warrens in House of Chains evinced, the Deragoth were once a numerous race spread across Seven Cities. The Jaghut Ganath supported this assertion in The Bonehunters when she asserted that the seven remaining Deragoth were the seven "surviving" Deragoth, implying there were once many more. In contrast, the Hounds of Shadow, while they may have originally been more numerous (ex: Pallick), were said by Tulas Shorn to have been created by a sentient hand with a pre-conceived role within the Shadow aspect.
It was stated by Mappo Runt in Dust of Dreams that a species of Plains Bear was utillized in the breeding of the Deragoth, and that the Ay were used in breeding the Hounds of Shadow. Though whether or not this was true and how Mappo would have known this was yet unknown.
It should further be noted that Osserc claimed in House of Chains that he originated the name "Deragoth", meaning "Hounds of Darkness" in the Andii language. He stated that they were not related to Mother Dark, that he merely thought the name appropriate based on their characteristics and that they had no connection to the pantheonic Darkness.