Exactly what the difference means literally. A shower is a shower, a bath is a bath. I'm not sure how we can help you, perhaps consulting a dictionary is what you need.

A shower is bathing with no water that sits in the bottom (running water over you and it goes straight down a drain). A bath is a tub full of water that you sit in and soak in like a hot tub. Most think of babies taking baths but sometimes adults and older people do too to relax,

Taking a bath is when you are in bathtub while taking a shower is in the shower, standing...