Difference between a tranny cooler and engine oil cooler?

The tranny cooler cools the fluid that circulates in the transmission. It is a different type of fluid and is separate from the engine oil. A trans cooler is a must have for towing, but I don't think you need to bother with the engine oil cooler. The engine coolant would overheat before you'd ever have a failure due to overheated engine oil. Most of it has a flashpoint of over 400*F. Synthetic is better in this regard and might be cheap insurance for high temp situations.