In everyday terms necessity and sufficiency are linked to the concept of "causality" which Hume showed was problematic.
In cognitive science the modern view is that "the brain" is necessary for "cognition" but insufficient to account for it.
In biology heart failure is sufficient to account for death but not necessarily the main cause of it.
Note that both of these assertions may be
subject to negotiation.
Context tends to govern semantics. A square
(mathematically) necessarily has four equal sides, but a square
(in town planning) need not. Contexts assume agreement about terms. Problems arise say when a theist proposes "God" as necessary for "existence" and an atheist claims that this is a vacuous tautology mimicking a mathematical definition.