Ubuntu Has Started Work On A New Desktop Snap Store
Developers at Canonical have begun committing to a new Snap Desktop Store. The first code commits were only last week, so it's not yet something for end-users to get all excited about but presumably they'll be aiming for it to be in good shape by next year's Ubuntu 20.04 LTS.
The current Ubuntu Software "Store" experience.
Most recently they have been making use of the GNOME Software Center but now there's this dedicated Snap Desktop Store in the works. As well, it's complementary to the web-based offering at Snapcraft.io for viewing available Snaps.
The original Ubuntu Software Store from a decade ago.
The C with GTK-written Snap Desktop Store is being developed at ubuntu/snap-store on GitHub for those wanting to track the progress. At this point I haven't seen any public road-map/plans for what they envision in their latest software "store" attempt besides now being this from-scratch Snap-focused software center.