The vowel sound in "nose" is the open-mid back unrounded vowel, represented by the symbol /o/. It is a rounded vowel produced with the tongue placed in the back of the mouth.

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The vowel sound in "book" is the 'oo' sound, which is a close back rounded vowel.

The four parameters of vowel sounds are height, backness, tenseness, and rounding. Height refers to the position of the tongue in the mouth (high, mid, or low), backness refers to the position of the tongue in relation to the back of the mouth (front, central, or back), tenseness refers to the amount of muscle tension in the tongue (tense or lax), and rounding refers to the shape of the lips (rounded or unrounded).

In RP, the o in coffee is a short open back vowel /ˈkɒf.i/ , whereas in General American speech one often hears either a long open back vowel /ˈkɑ.fi/ or a long mid back vowel /ˈkɔ.fi/

Wiktionary offers two audio fragments that illustrate this difference