Musicians like Clapton were at the forefront of British blues music when the style and feel was absorbed by young British bands from the records they imported and played to each other.
Blues morphed into rock music as players took the emotion of blues music and grafted a heavier and more up tempo sound, so that simply means that Clapton is both a blues and a rock guitarist, since he was on the ground floor of the UK development of both styles.
As advised, you need his early material for blues, especially his John Mayall period, and then simply move forward with him as he adopted rock music into his playing.
Music always has, and always will evolve and change, and some of these changes can only be ratified by looking backwards, it's rare for styles to have wholesale changes sweeping in, probably punk was the last seismic shift in UK musical styling.