What is the difference between indexing and abstracting?

Abstract - not practical, hard to understand, difficult
(Sentence: The atomic theory of matter is too abstract for most people.)

Index - a thing that points out or shows, a sign, token, or indication
(Sentence: A person's face is often an index of his mood.)

In summary, these two Words are not related.

If your question refers to the index and abstract as sources of information, then...

they are both reference works that reveal detailed information about resources. Indexes usually provide authors, titles or subjects of publications without comment, and abstracts offer a brief summary of content.