Unlike Robin in the comics, there's no scene establishing him in university presumably because he didn't go. However, there is is a scene with his high school coach right after his "accident" that turned him into Cyborg. I guess that Cyborg in the comics is in 18 and older range. In the series, there's nothing that gives us an idea of his age, but since he's with the others, we put his age at 16-18. People have theorized that he's the oldest of the Titans, meaning he's probably older than 18 in both versions. In the most recent adaptation(a live-action version), he doesn't even appear as a character, and Robin is a lot older than the rest.
Similar to Beast Boy, Cyborg shares little similarities with his comic version; the only thing they share in common is Cyborg's left eye, the biotic one. Also, Cyborg goes by his real name in the comics: Victor Stone. In the tv series, they focus on adding the color blue to his design, and the only human parts are his face and a small piece of his arms. In the comics, Cyborg's complete costume is white and has more individual sections, including a portion of his chest, his thighs, and the same small piece of his arms as his tv counterpart. I think the reason he's outfit is more white in the comics is for the stereotypical robot, but the design in the tv series, which includes blue and grey seems more fitting. The only other difference that's important to point out is that in the tv series, he's bald, but in the comics, he has short black hair.
Comic Cyborg is a bit more serious than his tv counterpart; he carries a lot of resentment and anger towards his father, which translates to most of his personality. He's outspoken and tends to stick to himself even though he sees the Titans as a support group. TV Cyborg is a very outgoing, funny, and cheerful character. He's very close to Beast Boy because they have a similar personality, but he becomes serious whenever the situation calls for it. He also practices a lot of understanding of characters similar to him. He considers himself as a freak, but he's grasped that there's nothing wrong with him because of his friends. Like Starfire, he doesn't have a large bias for another member, meaning he shows concern for all members whenever something occurs to one of them. Unlike Starfire, however, is he's pretty good at controlling his emotions. In the case of both Comic Cyborg and TV Cyborg, I think they go through the least amount of character development; for Comic Cyborg, it had to do with the fact he didn't have much storyline.
Cyborg's backstory isn't explored in the tv series, but in the comics, it's revealed that his father is the reason behind him becoming a cyborg. Victor Stone is born to a couple of scientists, Silas Stone(father) and Elinore Stone(mother). In the comics, they used Victor for experiments even when he was younger which lead to a growing resentment against his parents. One day while he was in high school, he went to visit his parents at their job, STAR Labs, where an accident involving an experimental portal occurred; a monster came through the portal and killed his mother, severely injuring Victor in the process. To save his son, Silas outfitted him with experimental prostheses. He was horrified to see what his dad did to him and wanted to die when he found out. Even after he grew comfortable with his new adjustments, it caused a lot of problems in his personal life: girlfriend at the time broke up with him for being a "freak", couldn't continue being an athlete, failing school, etc. He joins the Teen Titans originally to gain a support group for being a "freak". His father appears in the comics while he's never seen in the tv series. The Titans' Tower was given to them from Cyborg's father in the comics. TV Cyborg's backstory is similar to the Comic Cyborg's story until the part about the Titans. Also, in the tv series, Cyborg's the one who created the Titans' Tower. Just like TV Robin, there's no real mention of his backstory other than him telling the Titans' during the first meeting that he used to be an athlete.
Robin: They don't interact that much in the comics, and they don't have a relationship developed passed like acquaintances. Their only interactions were as Teen Titans, and they didn't seek each other out for anything else. In the tv series, Robin and Cyborg are close in a subtle manner. Robin tends to seek out Cyborg and greatly values the information Cyborg provides. While Cyborg is pretty outgoing, Robin lets his other side come out, and they can hang out without having to be constantly speaking to each other. They share a lot of similar hobbies, and they made battle moves that compliment each other. Cyborg, while I would argue he's closest to Beast Boy, trusts Robin a lot. After Starfire, he had the hardest time believing Robin betrayed them (Season 1) and agreed there had to be another reason for his behavior. Cyborg's also pretty understanding of the moments where Robin goes off without the team.
Starfire: Similar to most of the Titans in the comics, Cyborg didn't have a relationship with Starfire; their only interactions were on the battlefield. While Cyborg was living in the Tower, Starfire was living with Wonder Girl, so they didn't have any social time together outside of the Teen Titans. In the tv series, Cyborg and Starfire were close. Even though there's not as much development for this relationship as some of Cyborg's other relationships, I would say they're close. Cyborg likes to go with the ideas that Starfire has and is encouraging whenever she believes in something. He doesn't ever look at Starfire as a freak, and it's a reason they bond. Starfire has a bubbly personality and is naturally friendly to most people she meets, so Cyborg meets her halfway and is constantly nice and cool about things he might not even understand, like when she brings up her culture.
Raven: Again, I don't remember Cyborg and Raven in the comics having a close relationship. They did interact more than some of the other titans because they both were living in the Tower, but not that close that they would hang out. In the tv series, I would argue they were the least close out of the Titans. I don't think that means they weren't close because of the effort that went into building the Titans trust in each other, but they don't have any moments of just them two interacting. They fight a lot together on the battlefield because it's their usual formation, and Raven can carry Cyborg whenever flying is necessary. Cyborg's respectful of the space she needs and understands that she likes her quiet, but since he's close with Beast Boy, he tends to get still yelled at a lot. In Season 5, he's worried (along with the rest of the Titans) when she goes missing and values her as an essential member. As mentioned in prior sentences, I can't remember too many hangout times when it just them two, but he is willing to do anything for Raven like going into her mind.
Beast Boy: As you'll notice with Starfire on Robin's analysis page, I purposely left Beast Boy last because Cyborg's the closest to Beast Boy. In the comics, this is arguably the only relationship of Cyborg's that had any development. He was known as a lone wolf and didn't make that many appearances with other Titans, but I guess Beast Boy is destined to be his friend. Their personalities were different in the comics, with Cyborg being more serious and Beast Boy being his goofy self, so they had a bumpy start. However, they got close, and he was one of the only people who could say something to Cyborg without automatically getting a snarky response back. In the tv series, it was rare to see one with the other; they're the dynamic duo. They played video games together, trained together, cooked together, watch movies together, etc. Even with having different tastes, for instance, Beast Boy is a vegetarian, and Cyborg appreciates a good steak, they hung out all the time. Cyborg didn't look down at Beast Boy or treat him as someone below him, which immediately attracted Beast Boy, who had some rough relationships in the past. He goes to great lengths for Beast Boy and will even snap at the other members, mostly Robin, whenever they say something negative of Beast Boy. He also isn't afraid to call Beast Boy on not being serious because he knows it's only Beast Boy covering up his emotions. He means it well, and if there's a misunderstanding, he'll go out of his way to make sure Beast Boy understood him. He's an enabler to Beast Boy's dumb ideas, and more than not goes along with them. It's weird because Cyborg doesn't exist in the newest live-action version, but their relationship tends to be noticeably in the versions I've seen.
Terra: TBD
Wonder Girl/Kid Flash: Unlike Robin, Cyborg didn't know or care about Wonder Girl or Kid Flash before the creation of Teen Titans. He respects Wonder Girl and is encouraging when Robin goes MIA, and they need someone to replace him as the leader. They don't have a lot of interactions, but she tends to confide in him when she doesn't understand what the best next move would be, or how to get the other Titans to trust her. She only shows up in the comics, so there's not a comparison from the tv series. Kid Flash, on the other hand, evoked negative reactions. Cyborg had a bad temper in the comics and Kid Flash has anger issues. Kid Flash is usually looking for a fight, and more than not, Cyborg wants to be the one to deliver. Their animosity chills down the longer they're in the Titans, but they don't have much of a relationship besides that. In the tv series, Cyborg is the only one who has any real interaction with Kid Flash because he talks to him after his fight with Brotherhood Evil. Even with that brief conversation, I wouldn't even call them acquaintances.