This post discusses two words that because of their disparate meanings are not easily recognized as cognates, as well as a couple of others that are, as a result of disguised spelling, perhaps equally unlikely to be associated.
The words detailed here derive ultimately from the Latin verb prodesse, meaning “useful,” by way of prode (“advantageous”). The descendant French adjective prud, meaning “valiant,” was borrowed into English as proud but came to refer not only to esteem of oneself or another but also arrogance. It also pertains to exultation or spirited behavior or to magnificent display. (By extension, it also refers to a raised or swollen prominence, such as when referring to a scar.)
The state of feeling proud in the senses of both reasonable and excessive esteem is called pride, and one considered to have too much pride is called prideful and suffers from pridefulness. (In addition, inspired by the regal bearing of lions, a group of these animals is called a pride.) Meanwhile, prowess, meaning sometimes “bravery” but usually “skill” (generally in physical feats), derives from prud.
Prude, referring to a person of excessive modesty, also stems from prud. In that word’s sense in French of “brave,” it became part of the compound prudhomme, or “brave man.” The feminine equivalent, prudefemme, referred to noblewomen, who were expected to demonstrate propriety, but the first element came to pertain to an excess of that quality to the point of priggishness. The quality of being a prude is prudery or prudishness, and such behavior is described as prudish.
A related word not easily recognized as such is improve, stemming from prode and meaning “make better” or “make good use of.” An act of improving, or something improved, is an improvement, and something that can be improved is improvable. Self-improvement, meanwhile, is an act or process of attempting to improve one’s circumstances in life.