Source: Collins Dictionary
Definitions:
- incorrigible: not corrigible; that cannot be corrected, improved, or reformed, esp. because firmly established, as a habit, or because set in bad habits, as a child
- inveterate: firmly established by long continuance, as a disease, habit, practice, feeling, etc.; chronic
Examples:
Incorrigible: I was sent to Hennington Hills as banishment for being an incorrigible youth.
inveterate: Lucien, known as Lucy, is an inveterate liar who isn’t as good at it as he thinks he is.
The only similarity I see between these two words is the notion of someone being forever set in their ways. So what is the difference?