Both words refer to displaying the facial expression that indicates pleasure, amusement, scorn, or mockery. On its own, smile commonly suggests such an expression indicating pleasure or amusement: smiled and waved, but in context, it can refer to a contemptuous expression, more like a sneer. To simper is to indicate pleasure by one’s expression, but in a silly, self-conscious, or ingratiating way: a salesperson simpering at customers. The situation in which simper is used is often that of flirtation or trying to win favor. Simper is found in the company of words like “sweet,” “cloying,” and “fawning,” which emphasize the fake, coy, or servile nature of such smiling—at least to the eye-rolling observer.
Both words describe the state of mental confusion and surprise prompted by an encounter with something we don’t understand or can’t make sense of. The familiar adjective puzzled refers to the effect on us of something we don’t understand: She looked puzzled. Nonplussed refers to a greater degree of confusion, combined with surprise, that may render a person temporarily speechless and slightly disoriented: Her sudden about-face on this issue left her supporters nonplussed. It is common for someone to be left nonplussed or be nonplussed to discover, find, or learn something. Typically, someone can be, seem, or look nonplussed, be left nonplussed by something, or wear a nonplussed expression or stare. However, it’s also common for someone to be in this state only momentarily or for a moment.
High and lofty refer to something that has considerable height. High is a general term, and refers to extending upward or being at a considerable height: high towers; a high shelf. Lofty refers to imposing or even inspiring height, often in architecture or the natural landscape: lofty cliffs; a lofty spire; at a lofty height. These words also overlap in their figurative senses, so that you can elevate or exalt high ideals and ambitions by making them lofty ones.