What is the difference when the weather report says thunderstorms vs when it says thundershowers and the picture is still the same?
Physically there is no difference. A thunderstorm is defined by occurrence of lightning, no matter how much lightning there is, if it's cloud-to-ground or intercloud. Usually if meteorologists talk about thundershowers in weather reports they want to point out that there will be weaker thunderstorms (e.g. without hail, storm, heavy rainfall or the danger of flash floods).