Shogun pages can have a range of different statuses to indicate what they are currently doing. These are indicative of what they are currently doing.
When a page has been published. It will show the 'published' status, this means that the page is live on your store.
When pages are in their draft state, they will display the 'draft' status. This means that the page is still work in progress and that the page is not currently live on the store.
When a page has the 'outdated' status, this just means that there are edits that have been made to the page that have yet to be published to the live page. This is perfectly normal and nothing to worry about.
The 'running test' status related to the A/B Testing feature. This status will appear on pages that are currently running a test on the page.