What is the distinct difference between the 1968 dime with and without the mint mark?

The very distinct difference is that if it doesn't have a mint mark it was struck in Philadelphia. The P mint mark wasn't used on dimes until 1980. If it has a D mint mark it was made in Denver. Both are only worth 10¢ if found in change.

If it has an S it's a proof dime struck at San Francisco and only sold to collectors.