Potatoes are as much “vegetables” as carrots, radishes, turnips or yams. Why the reclassification?
As far as that goes, if dug up and the dirt is wiped off, potatoes may be eaten much like an apple. But nobody, NOBODY, will ever mistake a potato for an apple.
My horticulture prof once told me that a fruit is a mature plant ovary. The short form is that if it has seeds it’s a fruit. But try telling granny that a tomato is a fruit.
Botanically an Idaho potato is an underground stem while a yam or sweet potato is a true root.