Ah, the chibi style is for the show called Teen Titans Go! It has some mixed reviews.
On one hand the writers slip in some hilarious references to the actual comics that tickle the fans and on the other hand it pulls away from what really made the Teen Titan's animation so good. It's random and weird. A lot of fans of the DCAU (DC animated universe) have some bitterness with it because it replaced Young Justice.
As for what the characters looked like in the original show versus how they looked in the comics; their main designs are for the most part identical. There were a couple changes; such as cleaning up Starfire to look more innocent and more girlish than like the woman she was in the comics, and originally she was very scantily dressed and 'busty' with wild curly hair.
This is
roughly how she has looked all throughout her comic book life though there have been differences.

and her more classic design.

Starfire was the most dramatically altered, the others (Robin, Beast Boy, Cyborg and Raven) were for the most part unchanged except for some wardrobe variations.
Also as a fun fact the comics had Speedy, Wondergirl and Kid Flash as part of their team on a regular basis with other young heroes joining in as cameos. Also Beast Boy's other hero name is Changeling.
The Teen Titans as a comic book has had a long history and before DC's reboot for the New 52 had a wild ride with a lot of young heroes coming and going. I am most fond of the Teen Titans story arcs that were post the Dick Grayson Robin days (the team that the animation focused on). My favorite Teen Titans team is the one with Robin (Tim Drake), Superboy, Impulse and Wondergirl - popularized in the 1990s up to 2011.