To exaggerate something, such as the difficulty of a task, is to overstate it or to magnify it beyond the limits of truth. To embellish something, such as a story, is to enhance it with fictitious additions. While both terms deviate from what is accurate or true, embellish implies ornamentation rather than distortion. This sparkling nuance is a carryover from the other sense of embellish, “to beautify by ornamentation.” One may embellish a gown with beads or jewels to make it more beautiful, or embellish a story with colorful details to make it more interesting or compelling.
The noun arrogance is a commonly used term for overbearing pride or an offensive display of superiority or self-importance. The synonym hubris describes a more grandiose and excessive type of pride or presumptuousness that, in literature, propels a protagonist toward tragedy (a character who thinks they know better than the gods and therefore oversteps their place in the cosmic order will eventually fall, or, more precisely, be punished). In general use, the term does not suggest divine retribution, but it does carry a cautionary weight.
The adjective wrong is used in a few different ways. It can describe something that is not in accordance with what is morally right or good (a wrong deed), something that is out of order or awry (something’s wrong with your computer), or something that deviates from the truth or fact (a wrong answer). That third sense is where the synonym erroneous comes in. Erroneous means “containing error” or “mistaken; incorrect.” This adjective is commonly used to describe flawed reasoning or incorrect information. Erroneous originally described people or things that moved aimlessly or wandered about. While that sense is now obsolete, the idea of deviating or straying from a correct path, albeit a figurative one, still figures into its meaning.