Sort of but not really. In terms of what the neighbourhoods are literally called, you are correct - but the names represent historic development rather than represent anything meaningful in the present day. For all intents and purposes, "Midtown Manhattan" is NYC's true CBD and "downtown" - being the part of the city with the most development and the highest job concentration. The reason for this is essentially because of Penn and Grand Central Stations - their placement in Midtown, alongside with the breakthroughs in highrise construction at the time meant that Midtown became the premier development hotspot for the Island, and quickly overshadowed Downtown Manhattan as the more important center for the island. This can even be seen with how the NYC Subway developed, where initially the BMT built their main Manhattan Hub at Chambers Street with the tracks looping around the Williamsburg and Brooklyn Bridges. Not even a decade after the loop opened however, they had to redesigned that entire section to instead direct trains up Broadway to Midtown because they realized that that was a far more important destination to serve. To this day, Chambers Street sits as an overbuilt decaying mess that stands as a testament to poor long term planning and decision making.