urban area; urban district
Refers to the part of a city or region that is built up, as opposed to suburban or rural areas. Often used in contrast with 郊外 (suburbs) or 地方 (countryside).
都市部では家賃が高い。
Rent is high in urban areas.
Many young people live in urban areas.
都市部への人口集中が問題になっている。
The concentration of population in urban areas has become a problem.
The population is concentrated in urban areas.
The gap between urban and rural areas is widening.
市街地 emphasizes the built-up, developed section of a city (streets and buildings), while 都市部 is broader, referring to the urban area as a whole in contrast to rural regions.
都市部 is the more common, everyday word for 'urban area', while 市部 is a narrower administrative/statistical term specifically defined by city (市) boundaries.
都心 specifically means the very center of a city (downtown), while 都市部 covers the entire urban area, including areas beyond the center.
Compound of 都市 (city) and 部 (part, section).