The game description on the official site states that Arstotzka has "reclaimed its rightful half" of Grestin, implying that the city was split between the two countries but was annexed by Kolechia at some point. The Kolechian occupation is referenced later on day 27 when Arstotzka is willing to further cede Grestin. Regardless of the original owner, it is not stated whether the city was divided during the war or in the aftermath.
When the new border was established, many Arstotzkan citizens had to remain in Kolechia as no one was allowed to cross for six years. Finally, on November 23rd, 1982, a checkpoint was opened, which allowed Arstotzkan citizens to return home and families to unite. The checkpoint also provided another route for entrants from other countries to enter Arstotzka, some with valid intentions and papers and some who don't have either of those.
East Grestin is the part of the city that is on the Arstotzkan side of the border. Explicitly mentioned places in East Grestin are the inspector's apartment, the Pink Vice brothel, and the Get Big Town gym. The city also has a subway system. There are also places for the inspector to purchase food and medicine and a place for the detained immigrants.
West Grestin is comprised of the parts of the city that are under Kolechian rule and not much is known about the city. It is implied that conditions in West Grestin and Kolechia in general are not as good as in Arstotzka.