BRS is a character who started out as a random image by an illustrator. Ryo of Supercell noticed it, liked it, and created a song using Miku based on it. The song got popular and the illustrator joined Supercell. We then had a lot of models, OVA, RPG, and anime series based on the BRS name as it was popular and a new franchised spawned from it.
Beyond its origins as a song, it has no links to Voclaoid and your better off asking for information on the BRS wikia.