Originally Posted by Prof. Peabody
Mick and the boys got their start by copying the Beatles.
The Stones were some of the early white boy blues musicians, while the early Beatles did rockabilly and rock ad roll covers.
Stones: R&B and blues cover songs dominated the Rolling Stones' early material, ... having been "rooted in traditional verities, in rhythm-and-blues and soul music",... primitive blues typified by Chess Records' artists such as Muddy Waters, who wrote the song "Rollin' Stone" after which the band is named... (From Wikipedia)
Beatles: Rooted in skiffle and 1950s rock and roll,... (again from wikipedia)
The early Beatles covered such artists as Little Richard and Carl Perkins, among others, while as pointed out above, the Stones were influenced much more by the artists on Chess.
And please don't claim that "it's really all just the same thing". It ain't.