Alkali
The word "alkali" is derived from Arabic "al qalīy" (or "alkali"), meaning "the calcined ashes" (see calcination), referring to the original source of alkaline substances. A water-extract of burned plant ashes, called potash and composed mostly of potassium carbonate, was mildly basic. After heating this substance with calcium hydroxide ("slaked lime"), a far more strongly basic substance known as "caustic potash" (potassium hydroxide) was produced. Caustic potash was traditionally used in conjunction with animal fats to produce soft soaps, one of the caustic processes that rendered soaps from fats in the process of saponification, one known since antiquity. Plant potash lent the name to the element potassium, which was first derived from caustic potash, and also gave potassium its chemical symbol K (from the German name Kalium), which ultimately derived from alkali.
Alkalinity
Alkalinity roughly refers to the amount of bases in a solution that can be converted to uncharged species by a strong acid. The cited author, James Drever, provides an equation expressed in terms of molar equivalents, which means the number of moles of each ion type multiplied by (the absolute value of) the charge of the ion. For example, 1 mole of HCO in solution represents 1 molar equivalent, while 1 mole of CO is 2 molar equivalents because twice as many H ions would be necessary to balance the charge. The total charge of a solution always equals zero.