I'll try to keep this as simple as I can.
In a riflescope, the objective lens group transmits the image to the first focal plane in the riflescope. This first focal plane is located at the front of the inner tube, somewhere very near where the adjustment knobs are located. As we know, the image transmitted to the first focal plane is perfectly in focus for a certain portion of said image. The portion that is in perfect focus will be located at a specific distance from the objective lens of the riflescope. The portions in front of that distance or beyond that distance will be increasingly out of focus, the further from that focus distance they are located. This is much more visible for the objects located between the objective lens and the focus distance, than for the objects located behind the focus distance. Riflescopes without any means of focus adjustments have their focus set at a distance where most people would be aiming and the maker relies on the optical effect called depth of field to make most the image appear in focus, even if not perfectly in focus. That fixed distance is usually around 100 to 150yards or thereabouts.
This fixed focus creates a problem for precision shooters who ply their trade at distances other than the one used by the riflescope maker. Of course, the further away the target is from the set distance, the worse the problem known as parallax is. And to further complicate things, the higher the magnification used to focus on the target is, the worse the parallax is.
We all know what parallax is and how it manifests itself, here we are only concerned about differentiating the two most common methods of setting the proper focus.
In a riflescope, the objective lens is not a single lens, it consists of a group of lenses, singles and doublets. In an AO (Adjustable Objective,) rotating the front part of the bell actually adjusts the distance between the lenses in the objective group and thus adjusts the focus on the first focal plane. It is a rather simple system that works extremely well and has been in similar use in camera lenses for eons. It can be very precise and requires little additional hardware to work. The problem is that from position, it's a bear to use. For prone, known distance shooting, it's great; for varying distances, it becomes cumbersome to use.
The Side Focus method was introduced to address this last issue above. However, instead of directly adjusting the lenses in the objective lens group like the AO, the SF (Side Focus) system introduces an extra lens between the objective lens group and the first focal plane. This lens goes back and forth, adjusting the focus of the image on the first focal plane. This back and forth movement is effected by the use of the side focus knob. This system is more complicated, adds hardware and another lens in the scope and is more expensive and heavier. It is also not as precise as the AO can be; the movement of the lens is small compared to the rotation that can be found in a good AO design. This is the main reason I outfitted my March-X scope with that 4 inch side focus wheel; that provides me with much better focus control. That and it makes the side focus knobs easier for the arthritic left hand.
I hope this is the information you were looking for.