The link in the members' area is actually a link to your subscribed threads. You can subscribe to any threads, even those that you've not contributed to. In the upgraded forum you can find the link to your subscribed threads in the Quick Links menu. By default the forum is set to subscribe you to all threads you post in, but you can control this via your profile settings.
The 'My Posts' menu is actually providing access to your posts specifically in two separate ways - threads you've started, and posts you've made.