It’s the same sex linked barred gene that’s used to make Barred like Barred Rock or Cuckoo like a Cuckoo Marans. From a black sex link viewpoint it’s the same gene. What makes the major difference between cuckoo and barred is the slow or fast feathering gene. There are always other factors but simplistically put, if a barred chicken has the fast feathering gene the barring comes out with that scattered cuckoo look. If a barred chicken has the slow feathering gene the feather grows slower and comes out sharply barred. It’s the rate of growth of the feathers that determines if the look is cuckoo or barred, not the barring gene itself.
The Jersey Giant has Extended Black and may have either gold or silver. The Delaware will have silver and is probably Wheaten. Extended Black will dominate Wheaten so the chicks will be black. Silver or gold is irrelevant. So all the chicks will be black. Whether they are solid black or barred depends on the barred gene.
The Delaware has barring and the Jersey Giant does not. It’s important which is the mother and which is the father. The rooster has two genes at the barring gene pair and the hen only has one. The rooster will give a copy to all his offspring but a hen only gives that gene to her sons. The daughters only get what the father has. That’s what makes a sex link work. If the hen has the dominant gene, in this case barred, and the father is pure for the non-dominant gene, in this case not-barred, the chicks will be sex linked. Pure means that both of those genes are the same, where split means that he has one gene of both barred and non-barred in that gene pair.
The other part of this is that the result has to be seen in the down. There are some gene combinations where the sex linked part is right but you cannot see it in the down.
So if you put a Black Jersey Giant rooster over a Delaware hen you get black sex links. If you put a Delaware rooster over a Black Jersey Giant hen all the offspring will be barred, male or female. They all got a barred gene from their father. Just because all those chicks are barred does not mean they are all male. You have to determine that by some other means.
You cannot make a solid white chicken with just Silver. If the other genes allow it to express itself the silver gene will give a version of the Columbia pattern like the Delaware where the body is white but the tail, neck, and maybe some other feathers will be black. To get solid white you need either Recessive White or Dominant White. Even with Dominant White you need certain other genes present to get a solid white chicken. There are so many interactions between the color and pattern genes, various dominance and recessive or partial dominance, and so many potential modifiers it’s hard to say much of anything where there are not exceptions. The appearance of the chicken depends on a lot of different genes and how they interact.