As it turns out, these go hand in hand. If you go through the test suite, it'll generate an implementation report that you can easily submit. At the time of writing we have three implementation reports up, but we could really use more! Are you working on an ActivityPub implementation? Please submit one! Not only does it help ActivityPub get through the last leg of its standards process (we need to wrap up over the next few weeks!) but don't you want to look cool by showing up as an implementation on the implementation reports page? ;)
Note that it's perfectly acceptable to incrementally submit reports... if it turns out that your implementation doesn't pass as many items on the implementation report as you'd like, it's okay to re-submit later. (At the time of writing, my own implementation Pubstrate has a number of items marked as not passing that I'll be getting passing over the next few weeks!)
One note is that the test suite has two components: some of the tests are automated, and some of them prompt the user to manually test something and confirm/deny that it is passing. We would like to have full automated coverage in the future, but the working group agreed that since time is limited and interoperability is already being demonstrated externally through federation etc, this would be good enough for now. But it would be good to get more automated!
Anyway, we're in the last mile of getting ActivityPub out the door. And if you're an implementer, you can help us get there. Submit implementation reports, and help us, the world, ActivityPub's standardization effort, and your project's own vanity by getting an implementation report up there!