Old City was built somewhere in 13
th century and surrounded by a city walls. While they made city safer, they didn't left place for growth. People started to build their houses north of Warsaw. While it was very close, this area was granted its own city charter. Old City was called just Warszawa or Stara Warszawa (Old Warsaw), New City - Nowa Warszawa (New Warsaw). It changed at the end of 18
th century, when New Warsaw became part of Warsaw. At this time Old City was no longer bussines and administrative center of Warsaw.
Old City and New City are - since then - names of districts of Warsaw. Not necesarilly in administrational sense. Right now they are part of Śródmieście - downtown.
Both parts were destroyed during 2
nd WW and rebuilt in fifties, in the form close to that of 18
th century.