For the purposes of identifying the root cause of damp, a leak is considered to be the escape of mains or wastewater, whether fast or slow, however it was caused.
We differentiate leaks from penetrating damp, which is rainwater. Clearly people will habitually say a gutter is leaking. But to us this is penetrating damp, if it causes ingress, not a leak.
Leaks for insurance purposes are known as an “escape of water”, they tend to exclude long term escape of water but could include rainwater related leaks – i.e. penetrating damp. See insurance claims.