Is there any difference between "content" and "willing"? If there is a difference, I would like to know in what context would you use the word "content" instead of using the word "willing"?
In my experiences in everyday English it's fairly rare for content to be used this way, though I think anyone hearing "content to [verb]" would understand. The words content and willing are definitely not interchangeable in every situation, or even in any situation but this one.
I think that you could make a case that the words have slightly different connotations: a person that is willing to wait is someone that will wait if necessary, while someone that is content to wait is satisfied with waiting. But I don't think that there are any situations where using one wording would be natural and the other odd.