Well, I believe they are configured the same. I have them set to notify me of updates and I get a yellow notice on the Desktop when updates come in.
The only one I have gotten on the Surface lately is that lame dictionary update that will not update. On the desktop it works fine...no problem update the dictionary on it.
This afternoon I saw there were 6 updates in the Store when I went to the Modern desktop on the desktop computer ( not the yellow notice on boot ) and it installed 6 updates. So I started the Surface and went to the Modern desktop and there was no number on the Store icon like there was on the desktop.
It seems Store updates are seperate from Microsoft updates which do give me the yellow notice. Store updates for apps just has the number of updates showing on the Store icon.
The Surface received zero updates today for apps and the desktop got 6. I < know > I have the Sudoku app on both machines as well as Microsoft Solitaire. I saw one for Solitaire on the desktop this afternoon but not on the Surface.
Which is what prompted me to come ask
UPDATE: I just fired up the Surface and went into Metro and opened the Store and went into Settings ( don't believe I have done that before ) I synched the licenses and then told it to check for updates and it found some but not all the same one's I saw earlier on the desktop. But, if it's like many programs, you sometimes have to have one update before you get another and since I know I haven't been getting all of them, it's likely that is the case here.
At any rate, that did get some updates from the Store now.
THANK YOU VERY MUCH
Are you sure you have you Surface configured the same? The default in 8.1 is to have the Apps Update Automatically...
Things that you can do to force, Sync your Licensing then check for updates. Also you can try the extreme step of running wsreset.exe which will reset the store app...