Where Twitter focused on short, sharp messaging, Williams and Stone are returning to ground they previously visited at Blogger.
Instead of the simple chronological organisation of a blog, Medium revolves around collections - articles that share a theme and a design template. By default, the highest rated items are shown at the top of a collection.
Owners of collections can allow others to add items to their own offerings.
Medium is currently in a closed beta as far as posting content is concerned, but anyone can be a reader. A Twitter account is needed to give positive feedback on an item.
Mr Williams said "we're re-imagining publishing in an attempt to make an evolutionary leap, based on everything we’ve learned in the last 13 years and the needs of today's world."
"We know that most people, most of the time, will simply read and view content, which is fine. If they choose, they can click to indicate whether they think something is good, giving feedback to the creator and increasing the likelihood others will see it," he added.
Medium is operated by The Obvious Corporation, which was the home of Twitter before it was spun out as a separate company.
Page 2: Branch - a venture backed by Obvious - went into public beta this week.