"There are a lot of basketball courts downtown."
Translation:시내에 농구장이 많아요.
Yes, they are equivalent. 장 (root word for place/location) can be attached to almost any sport to refer to the designated place/venue where that sport is played. 배구장 (volleyball court), 수영장 (swimming pool), 야구장 (baseball stadium), 스키장 (ski resort), etc. Whereas the usage of 코트 is limited. You can't say 수영 코트 or 야구 코트, for example. 코트 is an English loanword so I suppose you can use it only for the sports that are played in a 'court', like volleyball, tennis, basketball, etc.