As a rule of thumb, use peppermint for sweet dishes (confectionery, desserts, cakes etc). Peppermint goes well with anything 'chocolate' - add some to hot chocolate, or to chocolate cakes etc. Peppermint is the preferred 'after-dinner' mint tea. It goes quite well in fruit drinks, like punches. (Hint: freeze some mint in fruity ice cubes to float on summer drinks.)
Use spearmint for savoury dishes (with lamb and veges, mint sauce, tabouleh, Middle Eastern recipes, meatballs etc). Spearmint goes very well with fruit - fruit salads, strawberries etc and with veges (potatoes, peas, carrots etc). I prefer spearmint in fruit punches (I think it's more refreshing than peppermint, but it's a matter of personal taste.)
I find spearmint far more versatile than peppermint. In fact, I rarely use my peppermint. I do use the chocolate mint, though! It's a derivative of peppermint, great in ice cream or chocolate sauces or added to a biscuit (cookie) recipe!
3 cups sugar
1 cup water
6 tablespoons chopped peppermint
Dissolve sugar in water and bring to the boil. Add mint and boil for 5 minutes. Remove from heat, let stand for 30 minutes. Strain and bottle. Use as a base for summer drinks.