I think "downtown" can also have somewhat mixed meanings depending on context as well. Growing up in smallish suburb, people used the word "downtown" there to refer to the busiest part of Main Street where a lot of businesses were, but after moving to New York, I had to get used to the fact that "downtown" was used to refer to "lower Manhattan", and what I would have expected to call "downtown" based on how I was used to it being used is referred to as "midtown".

This is why the fancy shopping in the UK is on "The High Street".

Except the terms that took hold in London are "West End" and "East End" rather than up-town and down-town.

It may have been used historically, but I cannot recall ever reading the terms in anything historical.

So I think, same principle, but different words.