The sphere is the degree of magnification, whether near or distance. Less is required for distance focussing, more for reading and somewhere between for pistol, desktop computer etc..

If you have astigmatism, your eyes produce a "squerged" image, (a square becomes a parallelogram), but for mild cases, the brain corrects this. The cylinder, tilted at an angle, feeds a corrected image to the brain and this correction is the same for both close-up or distance. When you first get astig. corrected glasses, because they over-ride your brain, you tend initially to get a squerged image and may, like me, take the glasses back saying they are wrong! After a couple of days, your brain re-adjusts to the now correct image it is receiving.

Prism, I do not really understand, but I think it is correction for cross-eyes.