The World Trade Center was never a "subcity" of New York City—it was a concentrated commercial complex situated in Lower Manhattan's Financial District. The original seven-building complex (1973-2001) and its current reconstruction occupy a defined 16-acre site bounded by Vesey, Liberty, Church, and West Streets.
Newark, by contrast, is an entirely separate municipality located in New Jersey, approximately 8 miles west of Lower Manhattan across the Hudson River. As New Jersey's largest city, Newark operates under its own municipal government, school district, police force, and tax structure—completely independent from New York City's five boroughs.
The confusion may stem from both being major transportation hubs and economic engines in the greater metropolitan region. However, legally and administratively, they exist in different states with different governing structures.