The butterfly effect describes disproportionate downstream consequences from a small change. Cambridge connects the phrase with chaos theory; in general use, keep the emphasis on a small initial change producing a much larger outcome rather than on ordinary direct causation.
A “domino effect” describes a situation in which one event causes a series of related events to happen one after another. Use it when the emphasis is on sequential consequences spreading from an initial event, not simply on two events happening at the same time.
A “knock-on effect” describes an indirect consequence in which one event or situation causes further events or situations. Use it for secondary or indirect consequences rather than the first direct effect itself.
A snowball effect describes accelerating growth: as the process continues, its size or importance increases faster and faster. It is related to cascading consequences, but its defining image is compounding growth rather than simply one event causing the next.
“At stake” means that something valuable is in danger of being lost. The guide stays with current documented meaning and does not add unsupported origin chronology.
A “black swan” is an event that happens despite people having thought it could not happen. Use the figurative sense for a supposedly impossible or profoundly unexpected event; keep it distinct from the literal black swan bird, and do not treat every ordinary surprise as a black swan.
Oxford defines “a canary in a/the coal mine” as something that gives an early warning of danger. This guide uses that current figurative meaning without claiming an unsupported exact first use.
A “chain reaction” describes a series of events in which each event causes the next one. In figurative use, focus on the causal sequence; the expression also has a literal scientific sense, so context determines which reading applies.