Technically, "gone" is an adjective in "She is gone", but it's the perfect form of "to go" in "She has gone".
So "She is gone" focuses on the state of her not being here, and "She has gone" focuses on the act of her having gone in the past.
Realistically though, the difference is very minor and they both convey the same piece of information, and it would never be wrong to interchange them.
In casual language, they'd both be said as "She's gone" anyway.