Clawfoot bathtubs are the original cast iron tub. They come in various styles. Including double slopped style. Slipper tub style, this is where one side of the Clawfoot tub is slopped for making it more comfortable to rest in. And classic roll rim where the rim of the tub is rolled down.
The Jacuzzi bathtub is a type of spa whirlpool bathtub. Jacuzzi became the name that most of the world now adopts due to Jacuzzi being the manufacturer that introduced the whirlpool bathtub to the USA in 1968. A Jacuzzi bathtub is a bathtub that adds air to water and shoots it through nozzles which can be directed towards various areas of the body to add to the relaxation process of bathing.
Free standing or pedestal bathtubs can be dated back to 1000 BC. A pedestal tub is a bathtub usually in the middle of a room with a built up pedestal where the bathtub can be affixed. It is a type of bathtub that you would see in a typical art deco design.
So why do master bathrooms of today have a roomier feel? Largely in part to the corner bathtub.
Walk-in bathtubs help the elderly or handicap with bathing. The seat makes bathing easier. Usually these come with a door that offers a water tight seal.
Baby bathtubs are just a much smaller version usually with a very shallow basin and a gentle slope. The slope of the baby bathtub is done to assist the parent or adult bathing the baby in keeping the baby's head out of the water. They have many different types some that are placed in your own bathtub. Some are designed for a countertop next to a sink. And finally they have some that are designed to span the bathtub resting on the ledge of you tub making bathing your little one easier.