"Green space" can better be understood as nature band-aids, such as berms, pointless setbacks, and ornamental shrubbery ensembles meant to shield or "soften" hopelessly bad urban design. You know you've encountered "green space" when it is meant to be seen only through a windshield or when using it gets you ejected by security.
A city (or, more likely, a suburb) with lots of "green space" might well be a city with very little actual nature."
The insightful commentary above was a reader's response to this article at the Atlantic's City Lab. The full article by Eric Jaffe is well worth a read.