The first type of tub I looked into is the Clawfoot bathtub. Clawfoot is a freestanding tub and are the original tub made of cast iron. Typically there are 3 styles. Slipper tub where one side of the Clawfoot tub is slopped for making it more comfortable, classic roll rim where the rim of the tub is rolled down, and double slopped style.
Spa bathtubs are very popular in the United States. Jacuzzi developed a innovative bathtub called whirlpool in the late 1960s. Jacuzzi whirlpool tubs are for both therapeutic uses and relaxation. The water is directed under pressure to different points on the body.
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.
The corner tub is a fixed style bathtub that obviously sets in the corner. This type of bathtub was introduced into the modern bathroom to optimize space and make "master bathrooms" have a roomier feel.
Elderly love the walk-in bathtubs. Often known as handicap bathtubs, these tubs provide handrails to assist the elderly or handicap. Typically they have a seat to make bathing more functional.
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.