Bildung (f.)
Although there is significant overlap, the word Bildung is used more commonly in the sense of personal development and becoming a well-rounded and intellectually mature person (eine gebildete Person, not to be confused with eine eingebildete Person, which means “a conceited person”).
The word is related to bilden, meaning “to form”.
Ausbildung (f.)
The word Ausbildung refers to education for a more specific purpose (such as attaining a degree or diploma).
Berufsausbildung (vocational training) is specifically geared towards imparting practical skills that can be used at the workplace.