I'm reluctant to enter into the fray, but.....
Understanding cadence marks should be simple.
John has arms.
John Jr uses his father's arms differenced with a label while his father is living. Upon his father's passing, the label is removed.
John the 3rd bears his grandfather's arms with a label of 5 points, indicating he is 2nd in line to the arms. Should either his father or grandfather die, his label changes to one of 3 points, now showing that he is first in line.
ONLY FIRST SONS BEAR THE LABEL, and it is always temporary and indicating the line of succession.
Only younger sons use the crescent, star, martlet, etc as cadence marks, and they are permanent to those younger sons.
If John Jr has a second son, Tom, then the latter would display the arms with a crescent. But no label, as there is no need for it.
Tom Jr would use his father's arms with that crescent, and a label overall (label temporary, as with the rule above).
But future generations offer opportunities for confusion, poor heraldry, or whatever, as nephews, uncles, cousins, will attempt to use the same cadnce mark. Tincture change can help, two crescents in fess, or in pale, etc.
And we can turn to borders -invected, engrailed, dancety, per fess, per pale, quarterly, the changes are infinite.
A little study (Robert Gayre's book is more than you really need, but worth reading) and a little imagination are all that is necessary.
Just remember that military axiom, KISS.