A red herring is a deliberately loaded gun that never fires — a designed violation of Chekhov's rule rather than a cousin of it. Mystery convention overrides Chekhov by making the misdirection itself the payoff.
Side by side
Aspect
Chekhov's gun
Red herring
Fires
Must
Never
Purpose
Economy
Misdirection
Relationship
The rule
Its deliberate breach
Audience feels
Satisfied
Fooled, then satisfied
What each one means
Chekhov's Gun
Chekhov's gun is the rule that nothing conspicuous should sit in a story unless it's going to matter. Chekhov stated it as a rule about removal — if the rifle won't fire, take it off the wall — and in current usage it also names the planted detail itself: the object that turns out to matter.