1. All this Buda and Pest stuff is confusing you.
Yes, today the city is called Budapest. But once upon a time, there were two towns: Buda and Pest (actually, three including Óbuda). In the 19th century they were united to form one big capital: Budapest. The part of town on the western side of the Danube, Budapest’s green lung with its lush hills and gorgeous villas, is called Buda, while the flatter and larger part on the eastern side of the Danube, where the lively heart of the city beats, is called Pest.