The two never interacted in canon, since they both come from 2 different sagas in the franchise, Chiaki from Super Danganronpa 2 : Goodbye Despair and Danganronpa 3, and Kaede from Danganronpa V3 : Killing Harmony. Chiaki died before anything with V3 so she hasn't heard of Kaede, though it is likely Kaede has heard of Chiaki, being a Danganronpa fan herself.
They are similar in that they both acted as the emotional support for the male protagonists of their respective games, Shuichi Saihara and Hajime Hinata and are common comfort characters in the fandom, and fan favourites by many. They are often shown as an OT3 or friendship pairing with Kyoko Kirigiri, as all 3 were Kodaka's implied love interests for the protaganists.
In the extra game 'Ultimate Talent Development Plan', they would have both met in the real Hope's Peak Academy, however the actual game does not show any interactions between the two. Their similarities include similar eye colours, talent themed clothing, backpacks, and their overall uniform is similar, pink seems to be the colour used most on each of their designs. They are also similar for their strong concern towards their classmates that cost their lifes, with Kaede dying by being executed for trying to help her classmates finding out the mastermind, and Chiaki playing the despair game that killed her when she thought that she finally cleared it and saved her classmates.
This ship seemed to sail as their designs look nice together and that they have similar traits. It seemed to have started as a crack!ship or a random character ship first, but developed some fans of it along the way. There isn't not much art or fanfiction existing of the pair, however headcanons and shippers seem to be more abundant.
For a generally rare ship, it developed a good amount of traction on Twitter, and now has a fair amount of shippers for its traits. Twitter user @saiiboz seems to be the first person to refer to the pair as Piano Tiles, however the ship was around before its name. Rival ships include Komanami, Saimatsu, Irumatsu, and Nanamiki
- The name Piano Tiles comes from a mobile game where the player taps or holds squares to earn points, playing notes of the piano along to a song as each level, or song progresses. Art of the two often reference the game. As with most Chiaki ships, it is a name of a game, and a piano reference with Kaede.