Laws are systems of rules meant to govern behaviour, enforced through social institutions.
There are typically two fundamentally different types of law:
Criminal law — Passed by governments to punish undesirable behaviour, aka crimes. Crimes against persons, property, justice, etc… Considered a crime against the public body as such. Modern interpretation — e.g. romans saw assault / rape / murder, … as a matter between parties, leaving eforcement up to the victims (or their families)
For serious offences the victim doesn’t have to complain — the state will prosecute anyway, the prosecutor represents the state. C.f. US case names: “The people / commonwealth vs. X”, or UK “The crown vs. X”
Civil law — Laws that regulate disputes between parties (people, groups, corporations) aka wrongs. Here courts are there to settle disputes, not determine whether you’re guilty of a crime (or lack thereof). Contract law, trusts, etc… The wronged party brings suit directly — prosecutors do not get involved (Cases are hence “X vs. Y”. Note that many legal situations involve both a crime and a wrong. And the outcome doesn’t have to be the same in both cases c.f. O.I. Simspon who was acquitted in the 1995 criminal murder trial, but “convicted” in the civil trial.
Criminal law is about punishment, civil law is about compensation to the wronged party. But enter punitive damages, where the responsible party has to pay a larger fine than is necessary to compensate the victim, as a punishment. The US legal system has this (this is where the ridiculous sums come from) but many other do not (i.e. Swedish legal system). Note the standards of evidence, procedure, tools, … (force) are often different between the two.
Also note that many countries have different courts for ciminal and civil matters. But some also have different courts for a lot of other things e.g. different courts for crimes / civil matters, and another court for appealing the decisions of government. ”Förvaltningsrätt-kammarrätt-högsta förvaltningsdomstolen”.
There are often multiple levels of court, where you can appeal a judgement to the next higher level. Different rules in different countries, but there is often at least some form of appeal available ”Tingsrätt-hovrätt-högsta domstolen”
Two main judicial systems in the worlds — Common law and Penal code systems:
Common law — The law is the law as on the books but also what all previous courts have said all the way back to the Magna Carta (Jury trials).