The 1.6 comes from the sigma family, so think fiesta zetec s etc.

The 2.0 is the Mazda derived duratec-he eg st fiesta mk6.

The Mazda and the sigma have different bell housing patterns. B6 just means 6 speed box. Doesn't mean they're the same box and tbh I'd been surprised if a focus runs a b6, seems a bit small