This is a really interesting (!!!) question. The words are certainly related, but they are not synonymous. Both words are subjective. There is no reality in which you can name any concept as objectively interesting. Following that thought, to state anything as interesting is necessarily a subjective claim. Similarly, to be interested is a personal experience. However, individuals are capable of recognizing a topic as potentially interesting, without experiencing any personal interest (i.e, being interested).
Interested: showing curiosity or concern about something or someone; having a feeling of interest.
Interesting: arousing curiosity or interest; holding or catching the attention.
The word interesting implies causing an affect on an external viewer. Conversely, "interested" is the state created by an interesting reality.
Nothing can be interesting without causing others to be interested. Similarly, one cannot be interested without having encountered something they experienced as interesting. The words are very related, although they stress different phases of a subjective experience.