The term "waistcoat" is generally a more specific one than "vest" -- it refers, literally enough, to a sleeveless garment that covers a man's waist, hiding the top of the trousers and the bottom of the shirt. In a vested or three-piece suit, the waistcoat is made from the same fabric and lining as the rest of the suit, creating a uniform stretch of cloth from the ankles to the chest. Worn separately, waistcoats and vests are flexible pieces of menswear that can fill roles in formal or casual wear alike.
Like the formal waistcoat, men's custom made suits can incorporate an unmatched (or "odd") vest. The look then becomes more dressed-down, almost playful -- suitable for a relaxed evening on the town rather than a serious business event. Patterns are also popular in odd waistcoats, providing a cheerful contrast to the jacket above them.