How does Teen Titans fit in with the Young Justice continuity?

I assume Teen Titans is faaar in the future (though, in the DC and Marvel universes there are a lot of plot holes). Why Batman is there, and young. Dick Grayson is young.

That’s why I think they have nothing to do. There should be at least 15 years between them, probably more.

I believe they are a little bit connected because Cyborg started out as a member of the Justice Leaque, then passing down to Teen Titans and back and forth. A post discussing this topic in particular can be found here. In the first answer, however, it states that Cyborg is exclusively a Teen Titans member but last year in the Injustice 2 video game, Young Justice and Teen Titans teamed up.

In my honest opinion, Teen Titans and the Justice League are essentially the same, except the former just has teenage members. I guess this was how they became affiliated with Young Justice in the first place.

However, I remember one of the Teen Titans episodes stating how the Teen Titans group formed in the first place. Starfire was captured by a group of dangerous aliens in space, but with her powers and all, she escaped and headed to the nearest planet -- Earth. There, she flew in a city where Robin (the Dick Grayson version) had just moved into since he no longer wanted to work with Batman and wants to instead go solo, fighting crime on his own.

The same kind of thing happens with Beast Boy, where he leaves the superhero team, Doom Patrol, and wants to find other superheroes to work with, but at the end of the day, Robin's story does not give reason for him to be part of Young Justice, simply because of Batman.

I guess @SumanRoy's answer explains the concept in the best way.

I apologise if I don't fully answer the question, but by answering as I have, I hope to bring forward new details and clean some of the surface.

The Teen Titans show is based in its own universe only taking inspiration from prior DC material. Young Justice is a loose continuation of Justice League/JLU/Batman/Superman: The Animated Series. Everything that has happened in those shows has already happened in Young Justice.

I do not believe DC will officially put Teen Titans in Young Justice due to the difficulty of merging the continuity. However, they seem to have used the Outsiders team as a Young Justice version of the TTs with much inspiration from comic run of TT's line-up. They have a big building (not T-shaped though) based in San Francisco, and operates basically independently from the League. Basically they used the Outsiders' name and small story aspect from original Outsiders, but used Teen Titans as the basis of characters and how they interact.

I think during the timeskip between season 1 and 2 of YJ Dick Grayson founded the Teen titans. This only makes sense because Beast boy joins the YJ in season two and later founds the outsiders. The time line of TT can definently fit 5 years because that is how long the timeskip was between season 1 and 2 of the YJ is. Which is the biggest reason why Nightwing is the leader of the YJ in season 2. During that time is definently is plausible that Dick founded the TT. Hard to wrap around but It fits perfectly based on the logic. So down below is exactly what the timeline is:

YJ S1 -> TT (entire series/5yrs) -> YJ S2 (dick becomes NW and is leader of YJ) -> YJ s3 (outsiders)

Teen Titans (2003) and Young Justice never existed in the same universe and do not fit together. Both shows use Dick Grayson (Robin) as one of the main protagonists. For Teen Titans, this is confirmed in the episode "Fractured" and the appearance of "Larry" (whose real name is Dick Grayson spelt backwards). Teen Titans is loosely based off the comic series The New Teen Titans. I say loosely because the lineup and characterisations were changed from the comic. Young Justice is a next-gen continuation of Justice League: The Animated Series. Teen Titans and Young Justice exist entirely separate from each other and share no overlap, with Teen Titans Go! episodes being the exception (but they are created for humor and are not canon content).

When it comes to other characters beyond Dick Grayson, it's a simple explanation. Cyborg was a member of the Teen Titans, but after the New-52 reboot, he was aged up, his backstory modified, and he became a founding member of the Justice League. Raven was never a member of the Justice League. She has engaged with them and has worked independently, but she always remained a Titans member. In fact, Raven was the founding member in the comics and approached Robin rather than the other way around.

For some reason, the writers continue to de-age the Titans members to fit the age of the current Robin. They also tend to recycle story arcs to include the new Robin (see: the Trigon arc, Slade/Terra's arc, etc.). The only character immune to this is Koriand'r/Starfire as she is one of Dick Grayson's love interests and therefore matches him in age. Dick Grayson remains the founding member of the Titans, but all main Robins (Dick, Jason, Tim, and Damian) have spent time at Titans Tower to train in team-building.

In the end, post-New 52, neither series is a part of the main DCU timeline. Teen Titans never tied in with other content, like movies or shows, and Young Justice now takes place on Earth-16. The latest DCU Animated Original Movies (Son of Batman, Justice League vs. Teen Titans, Teen Titans: The Judas Contract) are the current canon. The Titans members are roughly the same age as Damian Wayne; Dick Grayson is older than all other Titans, bar Kori; and there is no mention of the other Young Justice main characters in the animated films, yet.

This is probably more information than necessary, and I know others have posted briefer answers, but I hope this helps clarify the answers given.