Krios Prime, or Krios, was the inhabited prime planet in the Kriosian system in the Beta Quadrant, and was the homeworld of the Kriosians. The planet was located on the border of Federation space in the region between Sectors 21166 and 22079, near Starbase 117.
This planet was named after Krios, who ruled the ancient Kriosian Empire with his brother Valt. The brothers became divided over the love for a woman named Garuth so eventually their empire fell. Krios kidnapped Garuth from her homeworld, Valt Minor, and took her to Krios Prime, which started a centuries-long war between the two worlds. (TNG: "The Perfect Mate")
By the 22nd century, the Kriosians were under the rule of the Sovereign Dynasty of Krios Prime, a family known on hundreds of worlds. The royal guardsmen of the Dynasty were known as the Sovereign Guard. Their leader was known as the First Monarch, a post which Kaitaama ascended to in 2153. (ENT: "Precious Cargo")
In 2256, this planet's location was labeled on the star chart "Alpha/Beta Quadrant Overview" in the ready room aboard the USS Discovery. The star was located in the territory of the Klingon Empire. (DIS: "Magic to Make the Sanest Man Go Mad", "The War Without, The War Within")
By the mid-24th century, after conquering Krios and suspending Kriosian sovereignty, the Klingons established a colony on this planet. In 2367, the Federation was accused by the planet's governor, Vagh, of aiding the planet's rebels, who hoped to free the planet from Klingon rule. However, it was revealed that Klingon Ambassador Kell, in an attempt to split the Klingon-Federation alliance, was in league with the Romulans, who were secretly aiding the rebels with forged Starfleet weapons. (TNG: "The Mind's Eye")
In 2368, Krios and Valt Minor took their first steps towards ending an ongoing war as Kamala, the first female metamorph born on Krios since the mid-23rd century, was delivered for marriage to Chancellor Alrik of Valt Minor. (TNG: "The Perfect Mate")
It was never implied or otherwise indicated that the planet depicted in TNG: "The Perfect Mate" (and referenced in ENT: "Precious Cargo") was supposed to be the same as (or different from) the planet that was portrayed a year prior in TNG: "The Mind's Eye".
Though unseen in "Precious Cargo", the final reference to Krios was further complicated in a conversation between Trip Tucker and Kaitaama, when Tucker asks to visit (simply) Krios, causing Kaitaama to correct him by saying "Krios Prime". The inclusion of this trivia by the writers was unnecessary for advancing the plot, but suggested that there was more than one planet with this name, or, among other reasons, she was extremely proper about her planet's name, which easily follows the air of superiority she carried throughout the episode.
Furthermore, while both planets were called "Krios", in both dialogue and in script notes, visually, the planet's color changed, quite noticeably, between the two episodes in which the planet was shown. For that matter, "The Perfect Mate" also made no effort to reconcile, or altogether mention the prominent Klingon connection made in the planet's first appearance. An additional, and unrelated, script note from "The Mind's Eye" described the Kriosian Capital City as thus; "The architecture is simple, Spartan, very Klingon." The visual discrepancy between both episodes was reproduced for the remastered version of TNG.
On StarTrek.com, it was stated explicitly that there were two different planets and/or systems that shared the same name: "Krios".  In contrast, the Star Trek Encyclopedia (4th ed., vol. 1, p. 445) only listed a single entry for Krios. The planet was classified as a class M planet, which – by the 24th century – was located in Klingon space. The Kriosian system was named as a protectorate of the Klingon Empire. Furthermore, the Encyclopedia's entry for "Krios Prime" directs the reader to "Krios", indicating the authors treat "Krios Prime" and "Krios" as interchangeable.
According to Star Trek: Star Charts (p. 62) and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), Krios' primary was a G-class star.