I have seen the film. In fact, more than once. This is a masterpiece BTW.
Now, to the answer.
Yes, they were meant to be related, metaphorically. I haven't read the book, so based on the above answer I guess it's different in the book.
Anyways, in the movie there is a relation. We have to infer it, it is not shown directly. I will cite few examples, firstly take Hugo Weaving's character from the first story, he is the reverend, father-in-law of that story's hero. Its like this, in the whole movie, the actual negative character is Hugh Grant. Hugo Weaving either comes as his henchman or as other negative character.
In the first story, Hugh Grant is the one who has slaves and he is signing the contract with Hugo Weaving. Then, in Halle Berry's main story, i.e. the one about the fuel scam, Hugh Grant is the person behind the corruption and scam and when Halle Berry starts to investigate, he sends his hechman Hugo Weaving to kill her.
In the sonmi 451 story too, Hugh Grant is the master of sonmi and her friends. It is like a modern version of slavery, like in the first story. That same hero comes to rescue sonmi from her master. Upon learning the truth about the fabricants she leads the rebellion and is arrested. The Unanimity(future world government sort of thing) general, played by Hugo Weaving, then executes her. She and the hero stood against fabricant creation so the general had to kill her. In the first story the hero and his wife(future sonmi) stood against slavery.
Now lets come to the main character of the whole film, Tom Hanks. In the whole film Tom Hanks is portrayed as a selfish character. In the first story, the doctor Tom Hanks tries to kill the hero for his gold. The slave saves him. It's Tom Hank's theory that forms one of the basis of the movie: "the weak are meat and the strong shall eat". In the next story, when Robert Frobisher is wanted for assaulting Vivian Aers, he seeks refuge in a lodge/hotel, under another name. The lodge manager/owner Tom Hanks recognizes him and indirectly threatens him. So Frobisher is forced to bribe him. As he doesn't have any money, he is forced to give up his waist-coat, which he took it from his lover, Sixsmith. There we see a selfish Tom Hanks. In the next story i.e. we see some goodness in Tom Hanks character. He saves Halle Berry from being cuaght when she sneaks into his office for the documents. But he fails to express his love or feelings for her. He is assasinated. Hugh Grant instructs Hugo Weaving to do this job, fearing that Tom Hanks might help Halle Berry. In the next story, Tom Hanks is a crooked, gangster novelist/writer who kills the critic. That too in front of everyone. Then, in the sonmi story Tom Hanks comes as an actor. This actor is shown acting in a film as the main character. That very character is the publisher of the gangster Tom Hanks.
Then in the last story we see a changing Tom Hanks. He is first a selfish guy in the starting of the story. He watches his brother-in-law getting killed by the man-eating people(Hugh Grant). Here Hugo Weaving comes as ol Georgee, which is Tom Hanks's subconscious itself. His brother-in-law calls for help, but Tom Hanks listens to his selfish mind and stays low. But he gets sudden visions about his past lives, the mistakes he made. So, there is a struggle in his mind. ol Georgee forces him to kill Halle Berry. But at that moment, he(Tom Hanks) does not succumb to his evil subconscious. He gets a chance to correct the mistake(s) he did in his past lives. He won't kill her.
In the beginning of the movie he was selfish, but he transcends to a better human, in the last.