There was probably a time when it was that simple in England too but not so simple today. This post attempts to analyze the governmental units in England.
First of all, England is a country within the UK.
Under today's system of governmental breakdown, land in England is either
1. Located in an area called Greater London, or
2. Located outside the area called Greater London.
The land that is located inside the entity called Greater London consists of
1. The actual City of London, and
2. 32 other boroughs which surround that inner city, called London Boroughs
The land that is locate outside the entity called Greater London is divided into counties. These counties are further classified
1. As Metropolitan counties, if that county mainly consists of a major city, or
2. Non-Metropolitan counties.
There are (as of this writing) 82 Metropolitan and Non-Metropolitan counties. Of these, six are Metropolitan Counties, each with a typical population of between 1 and 3 million.
Non-Metropolitan counties are either
1. Shire counties, or
2. Unitary authorities.
There are 28 shire counties. A shire country has multiple districts within it. A shire county does not have to have the word "shire" in its name.
The remaining counties are of the unitary authority type. A unitary authority type of county does not have districts, but only one council for the entire county.
The whole of England is divided into 10 government office regions used by the central government. These large regions are separate from the counties themselves, and are superior to the counties from a governmental standpoint.