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.