Minecraft update on Xbox One?

Minecraft does get quite a few updates, either to patch things etc or to add things. All games need updates though from time to time though for similar reasons.

Anyway, updates happen regardless of whether your game is on disc or digital. The console checks for updates every time you start the game and sets of the update automatically if required. The update is downloaded from online so the format you have the game on doesn't matter.

Updates are free.

You can't play the game while updating is in progress. Bit they generally don't take long and once done you can play as normal.