If the testator passes away and children have predeceased him/her, the predeceasing child's portion goes to that child's estate. This is different from a bequest which awards only to children who are living at the time the testator passes away.
The idea of "then living children" means the children alive at the time of the death of the person making the will. It would not include children who passed away beforehand.
"To the then living children of my brother" means the children of my brother who are living at the time of the testator's death.
"To the children of my brother" means that living children and the estates of deceased children would all share at the time of the testator's death.
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This would only possibly create an "issue" if a child were to pre-decease your brother. If all children of your brother were living, then the language is the same. If one child was deceased but had then living children, the issue becomes what to do with the share of the deceased child. Under the first "living children" only the living children are allocated a share and the child of the deceased child get nothing.
Under the second, its not a clear and with out more in the document, California would default into the grandchildren stepping into their father's shoes.
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The reason for doing it this way is to divide the shares among the living children only, not among the living children and the heirs of any dead children. It is important to write will clearly to make the intent obvious.