I suppose that a county court is for civil matters for private parties to sue each other for general civil causes of action. A county court further has a small claims procedure/track for cases of an especially small nature (IE less than £10K in England.) A county court may limit costs awards to only the court fees rather than those paid for legal advice by the prevailing party.
A magistrate is the lowest level for trying criminal offences, typically summary criminal charges.
A crown court is superior to a magistrate court in that it is the first instance for trying the more serious category of indictable offences. But a crown court can also be used for more serious civil claims, ie for those that are for higher amounts.
High court is the court of next instance for appealing all of these other courts' decisions. (Both civil and criminal).
After the high court one must then appeal to the supreme court.
Then in parallel to all of these there are the tribunals which I understand to deal in specialised domains (property, housing, immigration) and are designed to be especially less formal so that one needn't necessarily have professional advice or representation to further one's cause in them.
One first goes to a first tier tribunal, then an upper tier tribunal in the respective chamber corresponding to the nature of their matter (housing, immigration, employment, etc.) And then appeals start getting into the court system. High court is the next step from the upper tribunals?
What is strange is that to apply for an injunction of reinstatement or an anti eviction injunction, one would typically go to a county court, but why not a property tribunal as for a rent repayment order?
And then there is the question of all of the different benches within the various courts.
Who fancies clearing all of this stuff up a bit?