It's a little ambiguous. The EBRPD website has a separate section/map/catalog on their website for each, but the total acreage listed for Tilden Regional Park clearly includes the nature area, and the official map for Tilden Regional Park lists amenities within the nature area and shows it on the main map (although with a different shading, which is not used for other neighboring parks). The same map also has a zoomed-in detail map of the area around the Environmental Education Center on the other side.

The map that the district uses in it's master plan and catalogs only shows one park called "Tilden", but the most recent activity guide also has activities listed separately under "Tilden Nature Area" and "Tilden Regional Park" ( http://www.ebparks.org/activities/rin/default.htm ).  In the list of visitor centers, there is "Tilden Nature Area: Environmental Education Center (EEC) at Tilden Regional Park...".

Personally, I grew up in Berkeley and had many many field trips and other visits to the EEC, little farm, nature area, Lake Anza, etc and those places were all just "Tilden Park". It looks really weird to see it cut in half on the map.