So if one man sired two separate children, to twin sisters, would the children be more like siblings genetically?

I just read a story of twin sisters giving birth on the same day and I started to wonder what it would mean if both children were sired by the same father or even twin brothers. Would either case produce children that are technically siblings?
I know by law the first one would be half siblings and cousins. The two sets of twins would only be cousins.
I forgot to mention that I am only referring to identical twins.