They are not the same thing. You can find all three, including emulsions, at Jungle Jims. I bought mine at the Eastgate store. Stores in your area may carry the extract but not the oil, which you may have to purchase from a pastry shop.
Made with alcohol for the most part. Always buy pure, not imitation extracts so the flavor will carry through, especially in candy and baked goods.
Oils are usually more higher concentrated than extracts, so you would need to use more extract than oil, if you decide to use it in your recipe.
One part flavoring oil is roughly equivalent to four parts extract, but this may vary according to the products used. To be safe, begin by substituting 1/8 teaspoon of oil per teaspoon of extract, then add more drops of oil until you’re satisfied with the flavor.
Now peppermint emulsions are made with water, not alcohol like most extracts. The flavor is wonderful and to my palate, very aromatic. Taste as you go along with the recipe.