The phrase "a different description of" is correct and usable in written English.
You can use it when you want to indicate an alternative way of explaining or characterizing something.
Example: "The author provides a different description of the character's motivations in the second chapter."
Alternatives: "an alternative portrayal of" or "a distinct explanation of".
Cosby also offered a different description of the nature of his relationship with Constand, which he described as social and romantic.
Then starting in the Reagan years, we see a different description of America: Only invest in those at the top, and let trickle-down economics take care of everyone else.
The relation between DTFs and mobilities is clearly established and the concept of direct force transmissibility, which offers a different description of signal transmission within a structure, is also introduced.
Saban had a different description of his defense.
When investigators called Miller for more details, he was allegedly slurring his speech and told cops a different description of the woman who he'd originally called about.
Axelrod quickly hit back with a different description of the '60s: "No, when Russia was our greatest foe, bosses could dictate on women's health & Etch-a-Sketch was a toy, not a political strategy".
Each demands a different level of sophistication, and might need a different description for the mathematical model of operational accessibility.
The New York Times story by Carl Zimmer on January 28 , 2010(http://www.nytimes.com) "Study offers an insight into dinosaur colors" begins with a slightly different description of the discovery: "What color were dinosaurs?
Mr. Ainsworth offered a somewhat different description of this facility, which he called "a large yard-type of area".
But "last month on Earth Day, he had a little different description of the fleet," Mr. Bush said.
British historian David Motadel's recent overview of Nazi-Muslim relations presents a quite different description of the Husseini-Hitler meeting.
