Let’s start with mechanical focus systems. They have a focus ring that is directly coupled to and moves the lens elements.
Focus by wire uses electronic signals to control focus. The photographer turns the focus ring but that doesn’t change the focus. Instead, turning the focus ring controls the motor(s) built into the lens. The motor(s) take their instruction from the movement of the focus ring, and the motor changes the focus.
Focus by wire gets its name from fly-by-wire systems used in aircraft. Except on small aircraft the pilot doesn’t move the control surfaces on the wings directly because it would be impossibly hard. Instead, the pilot presses a pedal or turns a dial and electronic motors move the control surfaces..
And because the aircraft is so big, any small errors are not relevant.
In cameras it is different because small movements can be seen and felt. This is true in still photography and in video.
And that has been the source of the criticism of focus by wire – that the systems are laggy and prone to overshoot.
The photographer turns the focus ring quickly, and the system plays catch-up.
Photographers report that they feel divorced from the focusing, which is the exact opposite of what one should feel when trying to take a photo that needs critical focusing. The pressure might be off in a studio or with landscapes, both of which are situations where the photographer has time to focus. But on the street or with any fast paced action, the photographer needs to feel that the response is immediate and consistent.
The situation is improving and some focus by wire systems have smooth focus changes.
It’s helpful to know how the focusing system is on a lens feels before you lay down money for it.