Fold: Knits (wool, cashmere, jersey, fleece etc) things that stretch These limber lovelies can not endure gravity’s burden, if dangled from a hanger they will be languorously distorted.
Hang: Woven (silk, cotton broadcloth, tweed, etc) things that wrinkle
These prim pretties prefer crisp suspension.
When folding, ensure every item is visible and accessible. A tidy, flat stack of folded knits will quickly become jumbled chaos if removal is requisite to retrieval.