To urge is to insistently and earnestly ask someone to take a particular action: urge someone to see a doctor. Urge suggests pressing or leading someone verbally, similar to the way an urge we have can move us to act. Exhort, from a Latin verb meaning “to encourage,” suggests a high or moral endeavor relying on passionate arguments to persuade. Exhorting may take the form of advising or warning in the effort to convince (“Ask not what your country can do for you…”), and it is often on a larger scale: a crowd, followers, troops, or readers who are exhorted by a leader. You might use exhort instead of urge when the context calls for this word’s particularity, but it is also used as an alternative to urge in everyday contexts: she exhorted her child to eat the oatmeal.
Aha! Both of these nouns describe a moment of clarity, when we intuitively discover the true nature or meaning of something. An insight often appears as something given or provided to us by another person, or by a book, documentary, or article: provides a valuable insight into the poet’s process. Even putting aside the overuse of insight (Thank you for your insights!), an epiphany is an insight on a much grander scale, so much so that many of us are more familiar with it as a literary device. Epiphany suggests a sudden revelation or realization of a truth of great significance to us, usually triggered, sparked, or inspired by something ordinary or commonplace. Typical adjectives used with epiphany are personal, sudden, spiritual, and life-changing. An epiphany is a personal paradigm shift, which changes the way one sees everything.
Both words refer to two or more things coming together to form one entity. Unite, the more familiar term, has a broad range of reference, from two people uniting in marriage to groups uniting to form a single unit with a single purpose. Although unite sometimes refers to actual physical combination of once separate units, it often suggests a figurative becoming as one. Coalesce is more commonly used for literal fusion. It suggests a growing together, intermingling, or blending so that, especially in the sciences, we see it used of liquids, atoms, clouds, dust, coalescing to form a single substance or object. Still, the figurative use of coalesce is the most common, particularly for groups of people: local groups coalescing to form a national movement.