In Medieval England there were many institutions that could be called "courts of law", and these fall broadly into three categories:
1. Church Courts enforcing Canon law
2. Royal Courts enforcing the common law
3. Local, Manorial and community courts enforcing manorial and local laws
Church courts would be institutions attached to the households of church officials at various different levels. They would deal with offences by clergy and matters of eclessiastical law such as heresy.
The Royal Courts, or "Curia Regis", dealt with both civil and criminal matters. There were limits of jurisdiction such as the 30 shilling limit for civil matters and the rule that unfree persons could not use the royal courts. The term "Royal Courts" covers the court of King's Bench, Common Pleas, and others including courts taking place in the counties outside London - civil trials in Nisi Prius, Gaol Deliveries (trials of felonies), early on the General Eyre (civil matters) and later on commissions of Oyer and Terminer (in relation to felonies to do with land wars and disorder in the counties).
The local courts would have included manorial courts dealing with issues between tenants and unfree persons in the manor, the courts of towns and cities, and local minor criminal courts and specialised courts dealing with local issues.