A tuxedo is something a man or boy wears to a black tie event, like a formal social occasion or evening out. A tuxedo is usually black, with a white shirt, and often worn with a bow tie rather than an ordinary tie you'd wear with an ordinary suit.
An undershirt, also called a singlet or vest in some countries, is a garment you wear under other clothes as an extra layer. Undershirts are usually white and have no sleeves.
An undershirt worn as outerwear is usually called a tank top.
A vest is a garment with no sleeves. A vest that you wear under clothes is usually called an undershirt. Vests as part of a suit are usually called a waistcoat.
The baby in the picture is wearing a knitted vest.
A waistcoat is a kind of jacket with no sleeves. Waistcoats can be made from ordinary fabric and buttoned up like in the picture, or knitted.
A wetsuit is a special garment that people wear in the water. People usually wear wetsuits when they are scuba diving or surfing. Wetsuits are made of a special material that keeps you warm, and protects you from getting cut by rough stones or coral in the water. Wetsuits are also slightly buoyant, which means you float better if you are wearing a wetsuit.