Similar outfits? Then Kirk's Starfleet must be distinct from Picard's or Sisko's, 'cause their outfits are really different.
I could buy that S31 might've been revived by Sloane, but a continuous existence over centuries? I don't buy it.
Except, they're not just similar outfits, they are the exact same.
Besides, the official Paramount word on the matter is that Section 31 is an organization that has existed for 200 years. Hell, the novels have featured Section 31 and there's even indications that it might be featured in the Abramsverse.