Budapest was created when the towns of Buda (13th century Hungarian settlement), Pest (2nd century Roman settlement) and Obuda (1st century Roman settlement) were joined in 1873. This was made possible by the first bridge, the Chain Bridge, in 1849.
Since people seem to talk so frequently in terms of, this in Buda, and that in Pest, the thought that possibly they have local government divisions too seems logical, but that would be too easy for Hungarians. There are 23 Districts within the city and each District has its own government. Very interesting if you want to do business here. What is legal on one side of the street, may not be on the other side of the street. Fortunately, there is an overarching government that brings a tiny bit of sanity to it. But things are so different from one end of town to the next, that it even gets darker a few minutes earlier on the west side of Pest than it does on the west side of Buda.
Right now I am staying near the Opera House in District VI
The old Jewish Deportation Ghetto and now the Party District is in District VII
The center of Pest tourism along the river front is District V
The center of Buda tourism is in Districts I and II
Obuda (worth a visit) is in District III
And to the Bulk Trash day; last week was District VI, this week District VII; so if you are in town this weekend you can still marvel at what people stack on the sidewalks.