In the US, 'coat' is a very general word. The one on the right is more of a 'trench coat' style. We basically will call everything either a coat or a jacket; often, jackets are shorter or they are made of nylon or some other type of non-natural material, but that's not a hard and fast rule.

They both look like coats to me. 😊

The one on the left might be described as a jacket, particularly if paired with a skirt or trousers. However it's long enough to be described as a coat. The right hand garment is definitely a coat.

Coats are generally longer and often have buttons. But remember different countries might have different ideas about the same word... For example what I call a jersey is also called a sweater in other countries. 😂

the leather one is a "raincoat"