Los Angelean Interpretation of "Park"

When I see the word "park" on a map, generally what comes to mind is an open space covered in grass, often with some trees as well as some play-related amenities (like swings) and perhaps a concrete court or two for sports. We have investigated the two "parks" nearest to us in Los Angeles, according to our handy street maps. The one slightly less close by is community focused, but it has little greenspace -- in fact it has more parking than grass -- and a community centre building which seems to be the actual focus. The one nearest to us is devoted to plant life, but it does not seem to be open to the public. It is filled with lots of garden-like spaces growing lots of interesting looking things, but you can't get in. In fact, one section of the fence that surrounds it is actually topped with barbed wire. I don't know if this is a repository that the city uses to grow plants it uses in other places, or if residents who don't have yards get to rent space and grow whatever they want. Particularly if the latter guess for the nearer park is correct, both of these are pretty cool uses of urban space. But they are not parks.