What Tree Is That?™ Mobile

Are the leaves twice as long as wide, tapered at the tip; the bark of the trunk with high, corky ridges?
CLUE: The fruit is purple and a berry-like DRUPE.

Are the leaves about as wide as long and heart-shaped; the bark of the trunk without corky ridges?
CLUE: The fruit is a small nut attached to a wing-like leaf.