Although Ghost in the Shell takes place in the 2030s, and Appleseed the 2120s, the jury remains out as to whether both series are supposed to exist in the same story universe.
More than a few common elements carry through, like the Seburo weapons corporation, and fictional countries like Imperial Americana, but other things don't jive, like the perfectly developed, human-like cyborgs of GITS (Motoko, for example) versus the unfinished, machine like ones that appear in Appleseed (e.g. Briareos), despite the fact a century of time should, if anything, have improved the art of cyberization. Every point can be argued in either direction though, which is why nobody knows for sure.
-- DID YOU KNOW? -- It's been said that Seburo guns were an inspiration for the weapons seen in both the Halo and F.E.A.R. franchises of Xbox video games.
GETTING TO KNOW THE SERIES