"Home fries" is large, maybe skin on, probably with some round edges from the sides of the potato. As if they were homemade (although they probably aren't). "French fries" in American means perfectly square, thin, shoestring style.
Depends on where you're eating honestly. Some places call long flat fries home fries and other places call just like cubed fried potatoes home fries. Basically any fried potatoe shape that's not shoestring French fries might be called "home fries".