The Castle Doctrine and Stand Your Ground are both principles related to having a duty to retreat before using force.
In some jurisdictions you have a duty to retreat from a threat, if it's safely possible, before using force against the threat.
With the Castle Doctrine, any duty to retreat you have ends in your home. You don't have to retreat from your own home.
Stand Your Ground takes that idea and expands to any place you have a right to be.
Neither justifies the use of force on their own. There are other elements involved than just the duty to retreat. And neither has anything to do with taking your weapons or reducing your jail time.
there is no duty to retreat, even if you could retreat.
Many states have enacted so-called stand your ground laws that remove the duty to retreat before using force in self-defense. Florida passed the first such law in 2005, generally allowing people to stand their ground instead of retreating if they reasonably believe doing so will “prevent death or great bodily harm.”
https://criminal.findlaw.com/criminal-law-basics/states-that-have-stand-your-ground-laws.html