Your "weed wacker" is a gasoline driven engine--it will put out some oily exhaust, as it's oil is mixed with the gas that it burns. However, most of the oil is burned with the gas, so the exhaust is mostly smoke.
Your airplane engine runs off of GLOW FUEL--not gasoline. Two different animals. The glow fuel has castor or some synthetic oil in it that doesn't burn very readily. This keeps the engine oiled and keeps it from burning itself up. However, this oil will be driven out (mostly unburned) with the exhaust, and create a gooey mess all over your plane. There is a reason they are called "slimers." Just get some good grease cleaner and clean the plane up at the end of the day!