In the most generic sense, templates are just objects used to create other objects from. Your start assembly or start part are 'templates'. Same goes for drawings - a drawing template is a drawing (.drw extension) that is used to create other drawings from. Typically it will already have some placeholder views created so when new drawings are created from it they will already have three views (or whatever.)
Formats are used by drawings to contain information that should be common to all drawings, and for the most part, not changeable from the drawing. Think of them as kind of visible 'through' the drawing, or even 'on top' of the drawing. Usually formats will contain things like your drawing borders, zone marks, title blocks, etc.
Since formats are loaded into session every time a drawing that references them is opened, changes made to a format will be immediately visible in any drawing that references them. The exception to this are tables. Tables on formats are copied into the drawing at the time the format is applied. Future changes to the tables on a format will not impact existing drawings unless the format is re-applied and the existing tables on the drawing are replaced.
