Kirby York

The answer to your question is Yes and No depending on how exact you want to be.This will be a little lengthy but necessary to understand the ambiguity but hopefully should give you the straight answer.

Ford's experiences of WWII made him appreciate the intrinsic worth of life in the military coupled with his interest in American history he searched for an army story to turn into film. He was drawn to the cavalry due to a series of stories written by James Warren Bellah and published in the Saturday Evening Post. Purchasing the rights he got Frank Nugent to write a script from one of these stories entitled "Massacre" loosely based on the Custer fight.
Nugent and Ford deliberately blurred the story, this indifference to historical truth became very evident in all six cavalry films Ford made, they also toned down Bellah's original story as the stories are rendered almost unreadable today by their racist invective to the Native Americans.
So Sitting Bull became Cochise the Sioux became Apaches and Fort Starke became Fort Apache.
Captain Kirby York is manifestly promoted to Lt Colonel in the final sequence of the film where he leads his troops onto another campaign.

This began what we now call Ford's cavalry trilogy however, he did not originally plan three films on the subject. His second She Wore a Yellow Ribbon was primarily made due to the huge box-office returns of Fort Apache and the growing popularity of John Wayne. SWAYR script was once again based on two of Bellah's stories and picks up with a little artistic licence where Fort Apache ended, a flying 7th cavalry pennant against a blood-red background with a voice over proclaiming "Custer is dead"
This film of course told the story of a completely different character Nathan Brittles.

In 1950 Ford signed a three picture deal with Republic primarily because they were the only studio who would finance his dream Irish blarney "The Quiet Man". However the studio demanded a "Ford Western" first (a guaranteed box-office success). Ford once again returned to a Bellah story entitled "Mission with no record" but this time got James McGuiness to write the script and told him to stay close to the Bellah story. You will notice that the noble and dignified Apache in Fort Apache has now turned into murdering rapists in Rio Grande, the eventual title of the film. Reasons given for this was Fords anger with a supposed Communist threat to the US and the Korean War, consequently the Red Indians simply became "Reds".
The Colonel in the Bellah story was called Massarene but Ford insisted on taking the character of Kirby Yorke (now with an added "e") from Fort Apache and move his story along a number of years and instead of his traumatic memories of Colonel Thursday give him bad memories of the Civil War when under Sheridans orders he plundered the South and in particular his wife's family plantation (incidentally based on Ford's wife Mary whose ancestors family plantation was destroyed in South Carolina by the invading Federal Army)

So finally, Yes! by Ford employing large dollops of artistic licence, blurring historical and geographical truth made the character of Kirby York the same guy in both movies, but No! if based on Bellah's stories which were two entirely different characters. That's the best and straightest answer I can give you.