According to the definition of "Free fall", which is "Downward movement under the force of gravity only.", free fall only occurs when gravity is the only force acting on an object. But here on Earth, whenever an object for example gets thrown off a building, its not just gravity acting on it, but air resistance as well. The only time an object is only under the effect of gravity, would be in deep space close to another object with mass. So does that mean, that techincally speaking, free fall never occurs on the surface of Earth?
You can get free fall in Earth's atmosphere as long as you move the air along with the falling object. This is how free fall is produced in reduced gravity aircraft.
The aircraft itself is not in free fall because it has to use its engines to overcome atmospheric drag. However inside the aircraft the air and occupants are at rest relative to each other and free fall can be produced.
However apart from this, or other special cases such as dropping objects inside a vacuum chamber, you are correct that objects falling in Earth's atmosphere are not in free fall.
Just to add to John's answer, consider that air drag goes with v^2, so at low speeds the air drag can be negligible. From experience, when jumping out of a plane you have 4 or 5 seconds of "pure falling" before you really start to feel the air.
Shot towers took advantage of this. They were towers with a pool of water at the bottom. Spoons of molten lead would be dropped from the top, and surface tension pulled them into a sphere. The hit the water and flash cooled before air resistance came into play and made them into teardrops. Presto, a nice round bullet.