What's the difference between Awa and Tokushima?
Very little, actually
Awa was the old name for the area that is now called the Tokushima prefecture. When Japan was reorganized from feudal domains into prefectures, the name was changed too.
However, many people still use the name 'Awa' in relation to Tokushima, or Tokushima culture. The biggest festival, for example, is called the 'Awa Odori', or Awa Dance Festival. The local dialect is known not as 'Tokushima dialect', but 'Awa dialect.' And Western Tokushima is known by most simply as 'Nishi Awa', or 'West Awa'.