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Why is there no apparent relation between focal length and physical lens size?
For example, the Nikkor 20mm lens has a physical length of 42.5mm! That's more than twice the focal length! And if you consider the sensor is not directly on the surface of the lens mount, the distance from the lens to the sensor must be almost 50mm.
That is because lenses are made of a complex set of elements that interact.
The focal-length would match to the lens size plus flange distance if it were made of a single optical element. This would make a lens which has strong aberrations which would lead to poor quality.
Telephoto lenses are by definition lenses which are shorter than their focal-length. Wide-angle lenses pose a design problem in that they often need a focal-length shorter than the flange-distance so those, like your 20mm, often use a reverse telephoto design in order to make such a wide-angle possible.
Zooms obviously complicate matters and you have lenses that become shorter as you zoom in or some that do not change length at all.
Focal length is based on a theoretical thin lens (a single element lens having minimal thickness). The focal length is defined as the distance behind the lens that collimated rays striking the lens will be brought into focus.
Modern lenses have several elements placed in groups that all converge or diverge light rays. The effective focal length of the entire system of a lens is equivalent to the aforementioned thin lens in terms of the distance from the lens' nodal point to the film/sensor plane, and is measured when the lens is focused at infinity.
On telephoto lenses, the nodal point is beyond the front element of the lens. Wide angle lenses, such as the 20mm lens you mentioned, are mounted further forward than the focal length of the lens and the nodal point is is between the entire lens and the film/sensor plane. A lens of this design is referred to as retrofocal.
