I think this distinction is not actually useful in real life, where 99% of the money problems are from certain types of gambling and not from others. When people discuss gambling, they aren’t talking about bingo games and school raffles, they’re talking about the thing most people mean by the word gambling.
If the root problem is greed how is making that distinction not useful in real life?
What does the type of gambling matter? If we focus on the core issues: greed and money problems -- over trying to "protect" [my emphasis] others from the bad gambling -- we end up helping them with adjacent greed/money problems. Labeling outside things as the problem is the problem. Help the people learn to master the inner compulsion towards these things (and other skills to help pull themselves out of dire situations); the rest is just trying to find an enemy to blame because helping others in a real way is hard.
In the same way distinguishing between heroin and codeine is useful. You can get addicted to either, but one sure makes it a lot easier.
Not sure I understand your analogy; Neither heroin nor codeine is a root cause of problems arising from the other.
Greed (in a generous def of the word, as in the wanting/desire of as much of the thing as possible [money in this case] quickly and/or easily despite the cost) is a root cause of many of the issues people create for themselves with gambling.