No
The REAL ID Act does not go into effect until October 10, 2018 for California due to an extension. Afterwards you will need a REAL compliant ID or a passport for domestic travel.
You can use any passport for ID purposes. If flying out of country a passport is needed at most arrival countries and to re-enter the United States you must have a passport. If you plan on traveling out of the US, might want to take the extra time and money and get a passport now. Very simple and fast online. Get the picture at the post office, since they are the ones that process the passport. It is good for 10 years. Have fun and best travels. Check dhs.gov/real-id for each individual state id compliance.
So the 2018 Law is not in affect yet?
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