The San Diego Zoo and Safari Park are not the same and the Safari Park is NOT in San Diego. It's in Escondido, California, about an hour's drive (30 miles) north of the San Diego Zoo, which is in downtown San Diego.
San Diego Zoo has its own parking lot in front of the campus, and it's free for visitors. They can also use the Balboa Park parking lot, which is also free. The San Diego Safari Park though is a privately owned parking lot and incurs a parking fee. $15 is the fee for general vehicles and $20 for RVs. Overnight parking is not allowed for visitors of either property.