A font is the complete character set of one type style, e.g., Helvetica Bold or Palatino Italic. A font family is all the related fonts. The Garamond family includes Garamond Roman, Garamond Italic, and Garamond Bold, among others. Type is further grouped by historical classification.
Type is specified by font and size. Each font can be set to virtually any point size. All the fonts displayed below are 36 points. As you can see, they have different optical sizes. Each also has its own personality. Here are descriptions of some fonts as representatives of their classification.
Also read the Rules of Type.
In typography neither the old style nor a new style matters; quality does.
Jan Tschichold, On Typography, 1952
Oldstyle
Transitional
Modern
Sans Serif, Grotesque
Sans Serif, Modern
Sans Serif, Humanist
Slab Serif
Engraved
Script
Other