Live Steam trains are 'model' trains that actually run on steam! Yes, they are real steam engines in miniature. (well, there are also diesel and electric trains too).
Generally, these trains start with G gage (LGB) on the small side, and go to 15 inch gage on the high side. Above 15 inch, they are generally considered to be 'real' narrow gage trains.
Most people in the hobby build/maintain their own engines (well, the 'diesel' engines are often bought pre-made), which tends to make this hobby very related to the metalworking hobby