Definition of augment by Dictionary.com:
to make larger; enlarge in size, number, strength, or extent; increase
Definition of increase by Dictionary.com:
to make greater, as in number, size, strength, or quality; augment; add to
I cannot find the difference because the definition of the 2 words are the same.
For example, "her secretarial work helped to augment her husband's income"
Wouldn't it mean the same if I replace it with increase?