Stick, adhere, cohere, cling, cleave can mean to be or become closely, firmly, or indissolubly attached.
Stick implies attachment by affixing; one thing or a person sticks to another, or things or persons stick together when they are literally or figuratively glued together and can be separated only by tearing or forcing apart.
When referred to things, adhere is interchangeable with stick <the mud adhered to their shoes> It is narrower in idiomatic range than stick but is the usual term when the attachment results from growth of parts normally distinct or separate.
When referred to persons, adhere usually implies deliberate or voluntary acceptance (as of the creed of a church, the platform of a political party, or the doctrines of a philosopher).
Cohere takes for its subject a collective singular or a plural noun that names things that stick together to produce a mass, a body, or a unified whole. But occasionally when the notion of producing a unified whole is to be stressed cohere may replace stick or adhere .
Cling usually implies attachment by hanging on (as by the arms, by roots, or by tendrils) and may suggest, often strongly, a need of support in one that clings.
In its extended use cling may add to the suggestion of need of support one of dependence, but at other times it suggests tenacity in holding on to something possessed, believed, or used.
Cleave implies closeness and strength of attachment; when applied to persons, it commonly suggests depth of devotion and fidelity in affection.