It's civil cases that have the lower standard of proof. Civil cases arise when one party sues another, typically seeking money, and they are claims in equity, where the defendant is alleged to have harmed the plaintiff in some way.

Criminal cases require proof beyond a reasonable doubt. Most things that can result in jail time are criminal cases. Criminal cases are almost always brought by the government, and criminal acts are considered harm to society rather than to (strictly) an individual. In the US, criminal cases are classified as "misdemeanors" or "felonies," but that language is not universal in other jurisdictions.