The questions you ask are complicated and take a long time to answer but I will try to do it shortly.
Yes, Curtis and Washington are correct. The Yavapai and Nde Apache were together from our earliest memory. This is what I believe as do the San Carlos Apache people.
When the Salado people began leaving the area that is now east central Arizona, another group of people began moving in, these were the Pai, (Yavapai) they called themselves the Kewevkapaya (people of the east). During the time the Salado were leaving and the Pai were arriving, another group of people began appearing from the north. These were the Nnee, the Nde, (Apache) Athabascan speaking people. From where they came we do not know for certain.
The Nde Apache intermarried with the Salado who stayed behind and also with the Kewevkapaya Yavapai.
The Kewevkapaya people settled the southern and western slopes of the Pinal mountains, the Dripping Springs and Superstition mountains, the Four Peaks and Mazatzal mountains also. The San Carlos Apache ancestors are a combination of the Salado, the Kewevkapaya and the Nde Apache people who came from the north.
One group of the Nde Apache came into and setteled in an area known as Tiis Ebah (later called the wheatfields) on the slopes of the Pinal mountains. Tiis Ebah means (cottonwood trees there) the people became known as the Tiis Ebah Nnee (cottonwood tree people) or the Pinal Apache. These people are my ancestors.
The Kewevkapaya also lived at Tiis Ebah at the same time. The Kewevkapaya and the Nde Apache were friends, intermarried, shared culture, fought battles together, raided together and defended their homeland together. Today, the majority of the San Carlos people are Pinal Apache from the Tiis Ebah clans.
A second group of the Nde people settled in the Tonto Basin, Mazatzal mountains, Salt and Verde river areas. They lived there with the Kewevkapaya. They were the Dilzhee e people (Tonto Apache) some of their leaders were Kewevkapaya Yavapai.
A third group settled in the Arivap area, they were the Tsee Zhinnee (people of the dark rocks) or Arivaipa Apache. These peoples origin may have partially been from some of the Tiis Ebah Nnee, Pinal Apaches.
A fourth group of the Nde Apache settled in the Apache Peaks area north of Globe. These people were the Bichi Lehe Nnee (fled to the mountains people) or Apache Peaks Apache.
Finally a fifth group of the Nde settled at Tiis Zhaazhe Bikoh (small cottonwood canyon) along the San Carlos River. These people became known as the San Carlos Apache.
The San Carlos people today are a diverse group from several different areas and origins, including a common origin with the Kewevkapaya Yavapai. Some Kewevkapaya still live at San Carlos today.
Other Apache who also came from the north but are not associated with the San Carlos Apache are the,
Dzil t'adn, Cibecue Apache.
Laan Baaha, The Western White mountain Apache.
Dzil Ghaa a, The Eastern White mountain Apache. Some of the Eastern White mountain Apache were also the Dzil Nchaa si an (Mt. Graham Apache).
The Tse Noltl izhn, Mazatzal Apache
The Dzil Dlaazhe (Mt. Turnbull Apache) also a combination of the Nde and Yavapai peoples.
And of course the Chiricahua Apache who were the most infamous Apache of San Carlos reservation and the surrounding area, but are not associated with the San Carlos people or reservation today.
They are the ,
Chokonen, also called Cho-kune, Tsoka-ne-nde people.
The Chihenne, also called the Tcihene, Tcihende, Cha-ha.
The Bedonkohe, known as the Aiaha, a small subgroup of the Chiricahua.
And the Nednhi also called the Nde-Ndai, Nde-nda-i.
Much of the confusion of the Apache comes because the white man called us and labeled us one thing, while we called ourselves something completely different. I hope this helps to sort things out a little better for you. This is what I believe.