A uniform can be any type of clothing that a person is required to wear, such as a police uniform, school uniform(polo shirt and khaki pants), ect. while a suit is a specific type of clothing. (in short; jacket, tie and pants - business attire)

I can't speak for every American, but I am 20 years old and I have never used (or heard) the word waistcoat. It sounds like British English to me. So maybe British people say "waistcoat" and Americans say "vest" The two Englishes are very different