The Story
Well, basically, Kaikan Phrase is about the band called Λucifer, but the incarnations of the series as a manga and an anime are very different.

The Manga
Sakuya is the leader of the band called 'Λucifer' He has interesting fashion sense, is rich, and decides within a nanosecond of meeting a girl that he obsessively likes her, and will protect her. He seems to enjoy intimidating her and making shocking sexual advances on the her in public. He always manages to get there in time to rescue the her from whatever danger she is in. The girl in question is named Aine. She, like most Mayu Shinjo leading girl characters is fairly timid, Sakuya seems to startle her very easily. Aine is very cute, but is not liked at school, and is often beaten up and/or nearly sexually assaulted at school and has to be saved by Sakuya. Really, I wish she would smack Sakuya when he makes his advances on her sometimes. But actually, despite his aggressiveness, Sakuya does seem to be a nice guy who worries about Aine ^^;;; I probably make him sound menacing or something, but he really isn't like that. He is just very expressive about what he wants. ^_^ Sakuya first meets Aine when she dashes out into the street after a flying paper containing some rather hentai song lyrics she wrote for a contest an idol was having. Sakuya almost runs her down in his sports car. It was love (?) at first sight ^^ Because Aine's song lyrics are good (and really suggestive and apparently perfect for Sakuya's band 'Λucifer') Aine gets recruited to be the new songwriter for the group. It's her hentai song lyrics that first capture Sakuya's attention, and it's her song that gets Λucifer noticed by the music studios :) Lots of intense scenes between Aine and Sakuya :) Lots of bishounen guys, and song lyrics that I *really* want to decipher! ^_^ So the manga focuses on the relationship between Sakuya and Aine as various forces try to come between them. Be it evil music producers, jealous old flames, new bishounen on the scene, Sakuya and Aine fight to stay together. There are some side stories about the other band members, but the spotlight is on the main couple. The manga is very smutty, but in a cheesy, silly sort of way. Like I said, it's a guilty pleasure, like romance novels :D

The Anime
The anime follows the members of the band Λucifer, from their very beginnings, when they leave their old bands, first meet each other, officially form Λucifer, to their eventual fame. It details the conflicts between the band members on the rocky road to fame as they try to make their 5 very different personalities into one unit as Λucifer. Many of the early episodes are about the band members trying to get Sakuya to join the group, and then after that it is the ban's struggles to get their name out as a band, become an indie group, and try to get a contract. They play everywhere from empty alleys, to music live houses, to warehouses, etc. This is much more of a story about the band as a whole. There is some focus on Sakuya, but the other members get major storylines too. Their characters are fleshed out so much more in the anime. Aine-chan isn't even in the anime until episode 22! Quite a change from the manga!