As for build numbers, you're looking at a bump up from build 3.6.1577 to 3.6.1580. We haven't noticed anything new or noteworthy while poking around the app, so it's likely that this update simply contains some bug fixes and performance improvements. Still, if anything new pops out after you update, be sure to let us know in the comments below.
We haven't yet seen the update land for the Windows 10 app, but we'll update this post if it arrives. In the meantime, you can grab the latest update to Groove Music on Windows 10 Mobile at the Windows Store link below.
Thanks for the tip, John!