These words have related meanings, as is suggested by their common Latin root (here, from haerere), which implies sticking or clinging together. One object adheres to another through the use of glue; a person adheres to a belief, a cause, a religion, or a political party. Cohere suggests the sticking together of items already present (The particles cohered to form a sticky mass) and the logical or natural connection of ideas and objects (Each part of his presentation seemed to cohere with established facts).
Dictionary of problem words and expressions. Harry Shaw. 1975.