Apple has quietly rebranded the iPhone Stereo Headset, dropping the device-specific iPhone name to transform it into the Apple Stereo Headset. This brings the branding of the Headset, which debuted with the original iPhone in 2007 but is now also compatible with the 120GB iPod classic, fourth-generation iPod nano, and second-generation iPod touch, in line with Apple’s more recent In-Ear Headphones with Remote and Mic and Earphones with Remote…