"Oven" is a very common, everyday word with a wide range of meanings. It commonly includes enclosed devices used to cook foods by heating them from all directions. Our kitchen stove contains burners on top, and an oven underneath. We also have a microwave oven. Pizza cannot be properly prepared in an ordinary home kitchen oven, it takes a special brick oven to cook it correctly.
A kiln is a specialized kind of oven used to dry and harden (to "fire") ceramic pottery, and also in industrial processes. The temperatures are often in the range of 1,000°C.--much higher than those used to cook food.
So, a kiln is a kind of oven, but not all ovens are kilns. If you talked about cooking food in a "kiln" people would laugh--it would burn it to a crisp. You can't roast a chicken in a kiln, and you can't fire a pot in a kitchen oven.
As a footnote, I honestly believe that the "n" in kiln ought to be silent--the word ought to be pronounced exactly the same as "kill." However, pronouncing the "n" is now so common that it is probably better for me to give up and say "the pronunciation has changed" (or possibly even "I am wrong.")