What is the shelf life of opened cheeses?
Yes, it differs by cheese.

As a very general and vague rule, the softer the cheese, the less time it will last.  Large chunks may last longer than small or grated pieces.

A ripe Camembert is at its peak for hours.  A nice chunk of Parmesan may last for weeks.

Dairy Googness summarizes as follows:


  
  Fresh cheese: a few days to 2 weeks
  Soft cheese: 1 week
  Semi-soft cheese: 2 to 3 weeks
  Firm cheese: 5 weeks
  Hard cheese: 10 months
  


Note:  my opinion on the above is that the firm and hard times are a little long for opened cheese.

Eat By Date is more conservative, suggesting only up to a couple of months for opened hard cheeses.

You can also freeze cheese with minimal loss of quality, which will substantially increase its shelf life.