The different options available within a typeface, such as roman, bold and italic, make up a type family. Times New Roman and Helvetica are examples of type families. These families are extremely useful because a designer can use just one or two within a project, but still have a wide variety of styles to choose from. This helps to achieve a consistent design.
Roman is the standard style of a typeface, not altered by weight, width, angle or any other characteristic. This is often used for large blocks of text, such as the text of a book.
Italic type is at an angle, generally slanting to the right from bottom to top. Italics are specifically designed within a typeface, meaning certain letters may be significantly different than the roman version to improve appearance and legibility. Oblique type, on the other hand, is the roman type slanted at an angle, as-is. The two are often confused.
Bold, or boldface, type is a heavier weight than roman type. As there is no official standard for naming typeface style, bold is often referred to as black or medium, or other names depending on the weight and the preference of the typeface designer.
Light type is thinner than the roman option. Depending on how light the type weight is, it will often be used at large sizes so it is legible, or to achieve a specific style. As with bold, there are light varieties such as ultralight.
Extended type is wider than the standard type of a family. It is useful for headlines and other large type areas, and provides even greater flexibility within a family.
Condensed type is a narrower face, which can fit into small spaces. Like extended, it provides more style options while staying within the same family.
Most type families will not just provide bold, italic, condensed, light, and so on, but combinations of each. This gives the designer even more options to work with. For example, Helvetica Neue is available in Regular, Italic, Bold, Bold Italic, Light, Light Italic, UltraLight, UltraLight Italic, Condensed Bold and Condensed Black. By using the options with a type family, and the combinations of each, designers can achieve a consistent layout while using a variety of styles.
Sources:Gavin Ambrose, Paul Harris. "The Fundamentals of Typography." AVA Publishing SA. 2006.