Please, for this uneducated one, what is " unwanted prizm", be it vertical or horizontal ?
When the Optical center of the lens is not centered over the center of the pupil, this creates prism. Prism 'pulls' the eye towards the base of the prism. Sometimes it is prescribed by the doctor to correct eso (inwards turning) or exo (outwards turning) eyes, or to correct hyper (upward turning) or hypo (downward turning) eyes, usually caused by muscular imbalance in the six muscles that control eye direction. When the prism isn't prescribed, it is 'unwanted' prism, and can cause the aforementioned problems, or at least eyestrain.
PD is pupillary distance, measured either from center of pupil to center of pupil (binocular PD) , or out from the center of the bridge of the nose. (monocular PD, which is more accurate) The PD is one of the two measurements used to set the optical center of the lens, the other being the OC height.
Your optician, if they are competent, will measure your PD with a pupilometer, a device that looks like Luke Skywalker's binoculars in Star Wars. They then will measure the OC height, which is done by marking the center of the pupil on the demo lens and entering this number into the lab instructions.
How are my bifocals different ?
The question is unclear. Bifocals have 2 different focal lengths; one for distance, usually at the bottom, and the rest of the lens is distance vision. Trifocals have three; Full reading, an intermediate segment above that that is 1/2 the power of the full reading power, and distance. Progressive addition lenses (AKA no-line bifocals) have a point (usually 2-4mm below the OC) where the add power gradually increases from 0 to the full add power.
When getting a eye exam, when is the PD measured ?
Some doctors will measure PD during an exam, and note it on the Rx, not all do. The Optician should always measure the PD for an adult the first time they see them; adults' PD rarely change. Kids PD's should be measured every time.
I thought the power number on the glasses related to how far, or should I say close up, you could see things clearly.
It is, but it is expressed in Diopters, not actual focal length.
Readers usually have the focal length set at 16 inches on down. For distances from 16 inches to 20 feet, this is termed intermediate vision, and commonly referred to as 'computer glasses'. Distances for 20 feet on is referred to as, not surprisingly, distance vision.
Hope this clears things up for you. (pun intended.)