For good - forever, permanently.
Forever - forever, eternally
More explanation..
"For Good" is often used when referring to something that has been happening so far, or until some point in the past, and from that time cease to happen.
( I returned back for good this time)
On the other hand,
"Forever" is often used with something that will continue to happen from the moment forward until the end of time so it is widely used with the auxiliary verb "will". ( I will stay forever with you )
Hope that helped! :)