Answer: They are related, yes. Although the variegated clones are apparently male, they are able to cross with wild growing females, thus creating a hybrid according to the following article in the American Journal of Botany. The authors suggest the variegated plants therefore also be considered invasive and removed from sale.
You would need to contact your local County Extension or the Department of Natural Resources to verify their legal status with regard to being listed as invasive -- or potential for being listed -- in your state.
I hope this helps you in your research.
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