Satisfy, content can both mean to appease desires or longings. The same distinctions in implications are also found in their corresponding adjectives satisfied and content or contented.
Satisfy implies full appeasement not only of a person’s desires or longings but also of his needs or requirements.
Content implies appeasement to the point where one is not disquieted or disturbed by a desire for what he does not have, even though every wish is not fully gratified.