Thanks so much for the explanation. The titling of the films are confusing.
I have had copies of all four Japanese versions and both American versions for a while, and can't for the life of me figure out the order and the context of any of them. I now finally can put them together in some semblance of contextual order.
in my opinion, the TV versions (parts 1 and 2) are the best since they are so stark and real and "flat" - who would have thought a made-for-tv horror anthology could have been so creepy and effective? Unlike many of today's horror films that are shot mainly in darkness and shadows, Shimizu is a master at creating contextual horror even in broad daylight. In juxtaposing time-lines, Shimizu creates visual tension and makes the audience work hard to get into the film, drawing them in only to deliver a one-two punch when the pay off, the reveal or the terror climaxes.
Some shorts are more effective than others, and some ideas (especially in JuOn 4) are particularly potent. Yes, American horror can learn a thing or two about the startling lack of blood in this horror series. It's just good old fashioned honest chills.

Nicee explanation. I wish I could find this version and the Ju-On 2 version somewhere, because to me, it was better than Ju-On: The Grudge 1 and 2, and The Grudge 1 and 2.

Thanks!

Nope. The start of the Ju-On/Grudge series begins with two horror shorts in a made-for-TV, 90-minute horror anthology called Gakko no Kaidan G ("School Ghost Story G", the G intended to mean Great). Shimizu wrote and directed for it. The two segments that eventually led to Ju-On are called Katasumi ("Corner" or as it was named on the director's cut of the US remake, "In a Corner") and 4444444444 (obviously, a lot of 4's, and it's a telephone number). Katasumi was the first appearance of Kayako; 4444444444 was the first appearance of Toshio and his cat. Both shorts appear on the director's cut DVD release of The Grudge, I believe.
In Katasumi, two girls are caring for the rabbits after school one day. One girl cuts herself, and so the other goes to get her a bandage. When she comes back out, her friend is nowhere to be seen and, well, I won't spoil the rest unless asked.
In 4444444444, a boy is riding his bike when a cell phone abandoned somewhere begins to ring. Curious, he finds and answers it, but only hears a cat meow. Eventually he hangs up. It keeps calling back, and then again, won't spoil it.
After that, the first full-length Ju-On movie was made, and it had a sequel. These are the movies known as Ju-On and Ju-On 2, or sometimes as Ju-On: the Curse and Ju-On: the Curse 2. Both were made for TV. I can't really detail their plots because I haven't gotten to see either (I've only seen Katasumi, 4444444444, Ju-On: the Grudge, and The Grudge) except a bit of the beginning of Ju-On. To my knowledge they haven't been released in America and if anyone knows that they have, PLEASE TELL ME!
Anyway the TV films were extremely popular, and so Shimizu was able to make the theatrical films. The theatrical films are the ones known as Ju-On: the Grudge and Ju-On: the Grudge 2.
The American remakes are known as simply The Grudge and The Grudge 2. The first American remake was basically the same storyline as Ju-On: the Grudge with different people (aside from the Saeki family, of course), a few omissions, changes, and I think parts of it were drawn from the made-for-TV movies (but don't quote me on that; again, I haven't seen them).
The Grudge 2, however, was very different from Ju-On: the Grudge 2. I haven't actually seen The Grudge 2 so I can't say a whole lot, but Shimizu himself said The Grudge 2 was very different from Ju-On: the Grudge 2; he said he didn't think he'd have directed it if it was the exact same story.
So, I hope that clarified things
Edit: Oh! I forgot to mention. There's also a Ju-On novel, simply called Ju-On, by Ken Oishi, and a manga called Ju-On: Video Side, by Miki Rinno. Both have been released in US. I haven't read the novel, but I have read the manga, and it's really good. I think it might include some things from the made-for-TV films, since I've seen a picture from Ju-On that looks exactly like a girl in one part of the manga (I won't go into details as to avoid spoilers, but this girl is, er, hard to mistake).