No its not they are different vegetables.
yes
no its a rhizome.
Rhizome is a STEM because the young leaves and adventitious roots grow from it.
Carrot is a root vegetable.
Yes. However technically "root ginger" is a rhizome, not a root.
j
Rhizome
Ginger (Zingiber officinale) is from the root or underground stem (rhizome).
A Root Vegetable.
Coptis is the underground stem (rhizome) or root of the plant Coptis chinensis.
Turmeric root. Rhizome
Perhaps you are searching for "sprout", "radix", "rhizome", or "tuber".