Technically there is no difference between “archived” or “completed” matters.
The completed report includes matters that have been archived.
The main difference is that archived matters can be filtered out on the matter home page.
The default timeframe for a matter to be converted from completed to archived is 14 days.
However, this can be changed at any time via Settings > Organisation Settings > Advanced and inputting the desired timeframe.
Disabling Auto Archiving
You can prevent matters automatically being converted to Archived via Settings > Organisation > Advanced and unchecking the box under 'archiving'