Yup SOCAL is a TRACON, covering (obviously) southern california. NORCAL is the Bay Area TRACON. The name of a TRACON indicates it's area of responsibilty.
LA Center is an ARTCC, covering a large part of the SW US. The name of an ARTCC just indicates where the facility is physically located (sort of, in the case of LA center, which is actually located in Palmdale.)
The SOCAL facility is in San Diego, but covers all the way from SBA down to Mexico. It is the busiest and largest in the world. Due to the the large number of airports, high traffic volume, and mix of aircraft types it's a great place to learn. If you can hang in SOCAL, you can hang anywhere...