Typography is the art, craft and design of typefaces. Typography is considered to have begun with Gutenberg's invention of movable type in the 15th century.
To quote Ellen Lupton, curator, graphic designer and author of Thinking with Type, "Typography is what language looks like".
interview with Ellen Lupton
Thinking with Type, example section
Typeface are the letters, symbols and numbers that make up a particular collection, font family. For example: Helvetica or Arial would be a typeface.
The correct term is face but font is used more frequently. A font is an individual face within a family. A font is one weight, width or style within the family. For example: Arial Narrow or Arial Bold are both fonts within the Arial family.
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