OK, I'll give it to ya as briefly as I can.
The Mitose clan is a Japanese family that ended up in Hawaii. They brought their family fighting art with them. If you trace the art back far enough, it probably has Chinese roots, but it was thoroughly Japanese for at least several generations. I really do not know the details about this.
The Mitoses passed on the art, and one student of James Mitose in Hawaii, was William Chow. Mr. Chow was an acknowledged powerhouse in kenpo, even tho he was only about 5'3" or so. Anyway, starting in about the late 1940s or early 1950s or so, Ed Parker studied under Mr. Chow. Mr. Parker brought what he learned to the Mainland, first teaching at Brigham Young university where he was a student, then teaching in California. Among his earliest California students were the Tracy brothers, Al, Jim, and Will. They began training with him in around 1957. I believe Will actually spent time training with Chow, and got his shodan from Chow, not Parker.
OVer time, Mr. Parker studied under various other people, including some kung fu people like Ark Yuey Wong, in LA. These experiences lead him to begin a long series of changes to his art and how he was teaching it. I can only assume that Mr. Parker felt these changes would improve the art, but the Tracys felt otherwise. They did not agree with the changes, and gradually split from Mr. Parker altogether and kept their version of Kenpo closer to what Mr. Parker taught them in the 1950s and early 1960s. At various times the split included a fair amount of hostility, but it is my understanding that by the time Mr. P died in 1990, they were on fairly amicable terms once again.
So in the mean time, thru the 1960s, 1970s, and 1980s, Mr. P continued to make changes and revisions and whatnot. Many people studied with him during these times, and their particular version of kenpo reflects when they trained with him. Few people actually stayed with him from the early days until the end. Out of this era came "Chinese Kenpo", which was I guess a nod to the Chinese influences that Mr. P was bringing into his art.
The later versions of his art, stemming from the 1970s onward, have become known collectively as Ed Parker's American Kenpo, or EPAK for short. I personally don't feel this is an accurate description because it assumes a large deal of unity and standardization from school to school, and I think that's not true. From what I have read in the forums, it seems those who were senior students at the end of MR. Parker's life often disagree about how things ought to be done, so I think there is really very little unity, even tho the curriculum may be fairly similar, at least on a superficial level. I prefer to simply look at the whole picture as different lineages that trace their roots back to Mr. Parker. This includes earlier splits like Tracy kenpo, and others like Larry Tatum, Richard Planas, Joe Palanzo, Frank Trejo, and our very own Ron "DOC" Chapel. At least that's how I see things. But at any rate, if you see a reference to EPAK, it refers to a lineage that probably started with Mr. Parker no earlier than about the late 1960s or early 1970s.
Getting away from Mr. Parker, there are other lineages that trace their roots back to William Chow without going thru Ed Parker. These include Kajukenbo, which was started in part by Adriano and Joe Emperado. They were students of William Chow in about the 1940s, and were senior to Ed Parker. Another would be Kara-Ho Kenpo, under the leadership of a gentleman in LA whose name I cannot remember. Some of his students post here, and I think he even shows up once in a while. He was a long-time student of William Chow.
Still other lineages trace back to James Mitose, without going thru William Chow. I believe they go by the name Kosho-Ryu Kenpo. I think it translates as "Young Pine Tree" or something, which is what the Mitose clan was calling their art. As far as I understand anyway, which I could be wrong.
Prior to James Mitose, it's hard to make any solid lineage tracing. I think the records earlier than that are just not clear.
However, there are other arts that also use the term "Kenpo" or more often "Kempo", some of which are related to the Mitose/Chow/Parker lineages, and some of which are not. An East Coast lineage thru Nick Cerio exists, and I think people like Fred Villari and Steve Damascos come from this lineage. I believe Cerio studied under some people and had some experience directly with William Chow and Ed Parker, but I don't think he was ever a long-time student of either. But I think this lineages use the term Shaolin Kempo or something like that. Another Shaolin Kemp Karate system exists on the West Coast under the leadership of Ralph Castro, who was a student of William Chow and somewhat of Ed Parker. But it is a separate system from the East Coast group.
There are also unrelated systems that simply use the term Kempo. Examples are Okinawan Kempo and Shorinji Kempo. The term Kempo is actually fairly generic, being a Japanese translation if Chinese Kuen Fa, meaning roughly "law of the fist". During the time when the Japanese karateka were changing the written character from "kara" meaning "Chinese", to a different written character "kara" meaning "empty", for karate - empty hand, as a way of distancing the Japanese arts from any Chinese influences as a movement of Japanese national pride, some arts simply kept the term Kenpo as a nod of acknowledgement to the Chinese origins of their arts. So they use the term, but there is probably no actual connection to the kenpo found in the US thru the Mitose/Chow/Parker lineages.
So there it is, as concisely as I can give it to ya.