These are the major Criminal and Civil Courts.
They will generally have a judge or judges running the trial. A Crown Court will either hear appeals form Magistrates' Courts, sentence criminals from magistrates or hold trials themselves. They often have a jury. These often take place with significant offences which the Magistrates' Court does not have the powers to handle.
County Courts are the civil counterpart from Crown Courts. Whereas a murder is a criminal case, something like a divorce or a claim for negligence is generally not a criminal matter. County Courts will divide cases between Small Claims (claims up to £5000), Fast Track (up to £15000) and Multi Track (over £15000).