I have never seen a Blu-Ray disk, and I am not too sure anyone I know has. You must live in the USA (not a device for connecting hardware).
The correct capitalization is Blu-ray. Also, are we going to argue the difference between disk and disc? Most (US) dictionaries list them as being the same. A disk can be defined as any thin, flat, circular plate or object or (when talking computers) any of several types of media consisting of thin, round plates of plastic or metal, used for external storage (magnetic disk, floppy disk, optical disk) (taken from dictionary.com). Admittedly, the BDA does use disc to refer to the media.
In general usage, disk and disc are synonymous (with k being preferred in US English, c in British).
Standard practice in computing, though, is for optical discs - Blu-ray, all the way back to Laserdisc - to use a c, while magnetic disks are k. It's to do with hard disks being pioneered in the US and optical discs being pioneered in Europe.