Though the Manga never actually splintered off with a "Z" - the Anime, and American Version of the Manga maintain the distinction between the two properties. Thematically, though, there was a HUGE shift for the series, with use and relying on Mythology and Martial Arts, now was introducing sci-fi elements, like aliens and time travel. Smoothly mixed together with the existing Dragon Ball world, we where now introduced to new facts: Goku is an alien, a Saiyan, who arrived on Earth as a baby (explaining his early tail, and ability to transform into a giant ape during a full moon). Piccolo was now a Namekian - an alien visitor from a far off planet. None of this is strictly ret-conning the already established story -- Piccolo and Goku's history, beyond being weird, or being labeled as a demon, was never previously discussed. I have to wonder if that was deliberately done so.
One thing about the series I wanted to mention, which I feel is a misconception (at least when it comes to the Manga version), is that events and fights don't necessarily take AS long, as was seen in the Anime. The TV series had to stretch out battles for episodes on end -- somewhat to buy time for the Manga to be continued and finished. A battle that takes place for endless episodes, for example, might be dealt with and handled within 1 or 2 volumes of the book series. (And thats only for major, top tier villains) I think Akira Toriyama has a tremendous sense of pacing, which goes unrecognized because of overshadowing from the Anime.
Another shift in the series was that Goku was now married, and was raising his first born child: Gohan! Gohan is at first a coddled little child - but upon the Saiyan Invasion, it was soon discovered that Gohan held tremendous power within his tiny frame. Goku, however, was not able to be there for his son - as he died in battle against his long-lost brother Raditz, the first invading Saiyan. It became clear that Raditz was only the beginning -- with fellow Saiyans Vegeta and Nappa coming on their way, upon learning the rumor of the fabled Dragon Balls.
Piccolo has fought Raditz alongside Goku, even though they still considered each other enemies. Upon Goku's death, and the Earth still being in danger, Piccolo took the initiative, telling everyone else to prepare -in addition to kidnapping Gohan, intent on training the young boy to his potential, to fight the powerful Saiyans.
Through this act of kidnapping, Piccolo was sudden thrust into the uneasy role of mentor. A harsh mentor, but someone who nonetheless taught Gohan how to be stronger. Being an ally of Goku, and now training Gohan, was the beginning of a softening of the character -- so much so that Piccolo would one day be good enough to restore himself with Kami, and become a single being again. That was still a ways off -- but the redemption and inspiring moral transformation of many, many hardened enemies throughout the Dragon Ball series became a vibrant and trilling theme. I literally can only count a few other heroes, who through sheer example, evolve and change the morality of their villains (Superman, the Flash, in some respects Spider-Man...)
Anyway - the Saiyans Nappa and Vegeta arrive on Earth and put the protectors of Earth through the wringer. Meanwhile, Goku has been undergoing extensive training in the afterlife, under Kaio, the Lord of Worlds. Once again, the idea of gravity is used as an explanation for why Goku is able to increase his powers so dramatically.
Upon his return to life, thanks to the Dragon Balls, Goku makes a triumphant return - though many of his friends where killed by Nappa during their fight. Piccolo, notably, died fighting alongside the powered up, yet still in-formidable Gohan. Goku handily defeats Nappa - to which Vegeta kills Nappa for his failure. For all the goodness Goku represents, Vegeta is his complete opposite. Vegeta gives Goku the fight of all time, but luckily comes through in the end the victor. Though, through Goku's mercy (and really, a desire to fight such a worthy opponent again) Vegeta is able to escape back into space.
The Dragon Ball gang's adventures soon take them into space, following Vegeta -- all the way to the planet Namek (Piccolo's world) Its here we find a deeper meaning to Vegeta's constant rage and ruthlessness -- as he has an enemy who he serves: Freeza. No more, though: Vegeta discerned that the Dragon Balls origins come from this alien planet, and he's correct: Namek has their own set of Dragon Balls. Freeza is quickly on the same hunt for the Balls, hoping to attain immortality, to suit his already incredible powers and vast interstellar army.
Bulma, Gohan, and Kuririn travel to Namek -- to find the planet under complete assault by Freeza's forces. The group where lucky, though, as Goku was right behind them - finally having recovered from his injuries fighting Vegeta, and was underway to planet Namek in a special space ship designed to (again) increase gravity around him, and enable himself to train like never before. When Goku finally does arrive, he is more powerful than EVER before! His eventual fight with Freeza, who lives up to his name as the most feared villain in the universe, rips the planet apart!
Using the Namekian and Earth Dragon Balls, the people killed by Freeza's men are revived - and everyone is transported off the planet. Everyone, except Goku and Freeza -- Goku desperately wanted to finish his fight with Freeza, who because of his cruelty of killing Kuririn, awakened a new form in Goku: Super Saiyan. His eyes light up, and his hair glows yellow -- not merely a cosmetic change - Goku fought with a fury he never knew he possessed before. Even though rage fueled this new form, Goku gave Freeza every opportunity to walk away, and not end up killed. Goku really proved himself a true hero when he does this, giving the unrepentant Freeza every opportunity to amend his ways. Goku's habit to reforming notable villains, though, has its limits. Eventually the planet Namek blew up, seemingly with Goku and Freeza still on it.
A year passes, and many people are revived with the Dragon Balls, along with Kuririn and others. When an attempt to resurrect Son Goku comes, everyone is surprised to hear that Goku is actually alive! He's off somewhere in space, and tells them through the Dragon God that he will return by himself soon.
The series takes a wild turn next, introducing Time Travel into the mix. Trunks, the soon to be born son of Bulma and Vegeta, arrives in the present to predict Goku's arrival on Earth. Before that, though, Freeza returns as a robotic shell of a creature - but with just as much malice towards the Earth as before. Trunks, however, proves a match for Freeza - wiping him off the map within minutes! Trunks is able to become a Super Saiyan -- though, no matter how powerful he is, he brings dire warnings of a new menace: that of Androids, created to kill Son Goku, and later the World.
The Android Saga seemed to up the level of violence to a high degree. We had seen blood and guts before, every so often, in the series -- but here we have broken necks, splattered guts -- the works. The androids are completely ruthless! During this saga Trunks reappears, and tried to change history by preparing the warriors for these battles. But Vegeta, who through sheer arrogance achieved Super Saiyan status himself, is humiliated to be defeated by one of the androids during this time.
The Android Saga takes an even wilder turn - when an even more powerful menace is unleashed: that of Cell -- a genetic being made with the cells of all the greatest fighters. He achieves new levels of power -- forcing Goku, Gohan, Vegeta and Trunks, to train in a mysterious Hyperbolic Time Chamber, on Kami's lookout. For every minute outside, 6 hours pass inside the chamber - so a lot of training is able to be done. Cell evolves much like Freeza once did - until he achieves his perfect state. He decides he wants a challenge, and creates a makeshift arena to fight upon.
Goku and everyone come to fight against Cell -- but to everyone's surprise, its Gohan who is pushed forward as the savior of the day, as Goku, when training with his son, felt how increased Gohan had become - surely able to surpass even himself. End of the day, though, Goku ends up sacrificing himself to save the world -- but its a world he knows is in good hands, with his son to protect it. Goku asks not to be revived - believing his presence on Earth was perhaps what brought so much menace to Earth.
Essentially, Toriyama was attempting to transition the series over to Gohan as lead player. I really enjoyed the new era - as time passed. Trunks of the future went away -- but Young Trunks was now growing up, and had a rambunctious playmate of Goten (Chi-Chi and Goku's 2ed child). Gohan grew up and began going to collage. Its here he meets his future wife, Videl - the Daughter of Mr. Satan (or Hercule, as he's sometime translated) Mr. Satan is an opportunist schemer, who took credit for Cells' destruction and saving the planet.
Eventually a new evil surfaced, called Majin Buu. Buu was controlled by a wizard named Babidi, and brought ruin to the Earth. Vegeta, also, sold his soul to Babidi, in exchange for more power. It ultimately lead to his death. Buu evolved quite a lot, first from an innocent dupe, eventually to an unquenchable being of evil. Gohan fought this creature, but eventually had to retreat for training in the afterlife where his father was.
The series had a great epilogue - as we are shown years later, the new Strongest Under the Heavens Tournament. Here we get to see Gohan and Videl married, with their daughter Pan showing the strongest competitors that she was no tike to be underestimated. Goku likewise is still alive - and was very eager for this tournament. You see -- in the final act of mercy to a nothingness-evil like Buu, Goku managed to put in a good word - and asked for Buu to be reincarnated as a good person. Sure enough -- Uub was in the tournament, meet Goku, and received an offer to train with him. Flying off with his new student, Goku flew off to adventures unknown.
I really thought that was a good ending to the series. From beginning to end, Dragon Ball is an enjoyable Manga which only gets better the more you get into it.