On the UK post codes, you’re pretty close to correct.
In the first part of the code, you’ve got 1-2 letters, which is the postcode area and usually based on a city name (W is West London in the BBC example). After the letters you’ve got 1-2 numbers (or a number followed by a letter, as in W1A). This gives a more granular division of the area, so it’ll often refer to smaller towns.
The second part is used to narrow it down to a small group of actual addresses, although the number and area it covers varies.
I went down a bit of a Wikipedia rabbit hole while checking a couple of bits about the format, and learnt that there are actually a few special cases/non-geographic post codes, including the postcode XMA 5HQ, which is specifically for letters to Santa.