Better character designs and developments. To be honest, the stern, cold major is a product of the 1995 movie and Stand Alone Complex.
In the original series she was still a professional, but a bit more laid back and personable. She had a boyfriend (who I think died at some point).
She became the stern, no-nonsense type after coming in contact with the ghost in the machine. At the end of the series her "Ghost" got lost in the net, I think. By the time she resurfaced she had changed a lot.
One of the major plot points in the Ghost in Shell series revolves around the cyberbrains. Basically in the timeline, people are able to imprint their brains into cyberbrains. These are purely mechanical and digital proxies that host the essence of a person. The thing is there is a thing called a "Ghost", and basically this is an unexplainable phenomenon that occurs with cyberbrains. You'd think that being cybernetic, you could easily clone someone's brain now that you can copy it, but it doesn't work that way. A person's "Ghost" is their spirit, and only the cyberbrain occupied by the "Ghost" is the real one, even if you copied the brain. No one can explain what ghosts are, why they occur or how to copy or create them.
This is basically where the story goes weird. The "Ghost in the Shell" the title refers to is a "Ghost" that seems to have spawned on the net that has no body, and has never had one. In essence it's a rogue soul that seems to have spawned out of nothingness, a phenomenon that is technically impossible. So a good chunk of the series is about Section 9 trying to track down this "Ghost" and capture it so they can study it and find out where it came from, but seeing as how it lives on the net, it's nearly impossible to pin down.