A suit jacket generally made of silk / cotton with embroidery work with rear portion made of satin cloth, which is worn over a shirt or a shirt or under a suit jacket.
vest: a man's sleeveless garment worn underneath a coat .
From The Louis Xvi Period Onwards Waistcoats Were Worn Under All Men's Outer Garments, Coat, Riding-coat, Frock Coat, Jacket, Etc. Usually The Two Front Panels Were Made From Fine Material And The Back, Which Isn't Seen, From Lining Material.
The fitted, long-sleeved upper garment could be made of either linen or wool. The most common type had shaping created by gussets at the hips.
A waistcoat (called a vest in Canada and the US) is a type of garment. Today, it usually refers to the third piece of a three-piece male business suit, to distinguish it from other types of vests. Once a virtually mandatory piece of men's clothing, it is rarely seen in today's world of casual dress.