This recipe calls for white dry wine, I only have white cooking wine. What's...

...the difference? http://allrecipes.com/Recipe/Shrimp-Scampi-II/Detail.aspx

That's the shrimp scampi I want to make. What is the difference?

Salt and in very large amounts. The product called "Cooking Wine " was invented during Prohibition as a way to allow cooks to still use wine but not allow them to consume it in sufficient quantities to get high from It is truly a vile product .
If you chose to use it do not add any salt anywhere else in your dish and be aware of the fact that reducing the volume of liquid will increase the amount of salt in the dish .
Another solution would be a vinegar that has been further diluted w/ 8 parts of water in order to closely match the pH of wine

Cooking wine normally has salt in it. Best bet is to use a dry white wine you would actually enjoy drinking.