Berlin's official geography is twelve Bezirke, each of which is enormous and tells you almost nothing. Nobody says they live in Friedrichshain-Kreuzberg. They name a Kiez: a few streets around a square, a U-Bahn stop, a park. Graefekiez, Reuterkiez, Samariterkiez, Boxhagener Platz, the Bergmannkiez.
The distinction is practical rather than sentimental, because Berlin changes character fast over short distances. The two halves of Kreuzberg, the dense, loud SO 36 around Kottbusser Tor and the quieter 61 around Bergmannstraße, are a twenty-minute walk apart and feel like different cities. Neukölln at the Landwehrkanal and Neukölln at Hermannstraße are not the same either. Choosing by Bezirk means accepting a range you could have narrowed.
This shapes how you should read listings. An ad saying “Friedrichshain” is telling you much less than one naming Samariterviertel or Boxi, and the Kiez name is usually the more honest signal. It is what someone writes when they are describing their actual life rather than optimising a search. Where an ad names only the district, the nearest U-Bahn station is the next best clue.
It is also the right unit for deciding where to look. Rather than picking a district and hoping, pick two or three Kieze whose character suits you, learn roughly what they cost, and watch those. Berlin is well enough connected that being slightly further out in the right place beats being central in the wrong one.