The word downtown is one that arose in American English, and originates in the geography of Manhattan with it's not-quite-true north-south grid layout. The city grew from an earlier settlement at the tip of Manhattan, where before the rise of midtown as the home of rising office towers this southerly area housed the commercial core of the city.

The word downtown itself "first appeared in dictionaries in the 1900s" but to this day it is a uniquely American word. In the UK, you have the city centre, in Germany the zentrum, in Polish centrum or śródmieście (literally the city centre) and so on to describe a city's central business district (CBD).

Uniquely in North America, the downtown of Philadelphia is called center city as opposed to downtown.

Downtown: Its Rise and Fall, 1880-1950 by Robert M. Fogelson.

Greetings all. We've had to do a big cleanout in this thread. Responses comprised of nothing more than examples of other terms used for cities around the world is not helpful. Just a reminder that responses in this sub should strive to meet subreddit standards, as described in the rules