Focal Point: The point toward which all rays parallel to the lens axis converge.
Focal Length: The distance from the lens center to the focal point.
Focal Plane: The plane where all light originating from a given distance from the lens will be in focus.
    In a camera: The film, CCD, Tube

Focus: The condition of a point source of light being represented as a point source image on the transducer.
 

No lens is perfect. They all have imperfections and produce abberations.
    Chromatic: Different wavelengths (colors) focus at different planes
    Spherical: Different parts of the lens refract the light to different degrees.
    Barrel and Cushion distortion.

We compensate with special coatings and compound lenses. Single lenses are just schematic diagrams. The real things are more complicated but they still have:
    focal point
    focal length
    focal plane

We describe lenses by referring to focal length. 28mm lens for example.

Focus can be thought as related to quality of light or more accurately, quality of the representation of the desired object on the transducer surface. What about quantity? How much light gets to the film or tube or chip?

Amount of light is controlled by:
    How big the hole is and how long we keep it open or aperture size and shutter speed.

NFL is all there is from now on. Automotive analogy of gear choice vs power vs speed vs economy. Various combinations can achieve the same apparent result.

Just a sample: Smaller lens openings reduce spherical abberation but introduced more diffraction.

Shutter speed:
    Motion pictures shoot 24 frames per second so each frame can be exposed for no more than 1/24 of a second.
    Most shutter speeds are less (much less) than a second. They are based on a geometric progression that halves or doubles the time of exposure with each step along the scale.

Change:    1        1/2        1/4        1/8        1/16        1/32        1/64       1/128        1/256        1/512        1/1024
(Seconds)

 Shutter:    1        1/2        1/4        1/8        1/15        1/30        1/60       1/125        1/250        1/500        1/1000
(Seconds)

Notice that the designation of shutter speed on the camera is actually a rounded version of the geometric progression. The change progression is based on doubling or halving the speed with each step. The actual shutter speed scale is not exactly true to the geometric progression.

Aperture Opening (Lens speed) f

f = Focal Length / Diameter of Aperture
Notice that the larger the hole, the smaller the f number. Thus, which would  let in the most light f22 or f5.6?
 

Again the numbers are a geometric progression based on the doubling of the amount of light with each step.
Doubling the diameter quadruples the amount of light entering the system. (Remember the Law of Inverse Squares?)

The multiplier that doubles the amount of light is the square root of two (1.414).

The series is generated from the same progression as shutter speed. If the number 1 represents the maximum opening, then each subsequent step cuts the amount of light in half.
Change:     1        1/2        1/4        1/8        1/16        1/32        1/64        1/128        1/256        1/512        1/1024

f-stop:        1        1.4        2        2.8            4            5.6            8            11            16         22          32

Note that the f-stop number is a rounded representation of the square root of the demominator of the change fraction. An f-stop of f 4 designates an aperture opening that is 1/16th the size (area) of the maximum opening (represented by 1). f 22  represents the rounded square root of 512 which is actually 22.627.  Yeah, I know it should be rounded to 23 but, contrary to what we are taught in early math about rounding, these numbers are rounded in some odd ways. Sometimes it is a matter of avoiding confusion susch as between 23 and 32.