You know, I'm not sure myself. Looking at the two parks I've tagged, I'd say my strategy so far has been to tag only the off-leash area when it's part of a larger park (https://www.openstreetmap.org/way/981107309), but with a dog park that is separate from any other park I've tagged all the "park area" as a dog park (https://www.openstreetmap.org/way/1123268840). Looking at the second one, I guess I didn't include the parking lot though, so I may eventually go back and expand the area to include it, since the park is what the parking lot belongs to.