Do all taxpayers in San Diego County, California have until June 17th to file their returns?

Yes. The IRS announced , Individuals and households that reside or have a business in San Diego County qualify for tax relief. 

IRS.gov

How about California state tax return? Is it the same case? Do I have until June 17th to file and pay taxes if I live in the San Diego county?

Yes, the Franchise Tax Board has also followed the IRS's guidelines.  If you reside in San Diego County, you also have an automatic extension until June 17, 2024 to file your state return.

Please see this link for more details.

@pkim8728 

Do all residents of SD county automatically qualify for the relief like last year? Or do I have to file or need evidence to qualify?

Does this extend payment due dates?

Yes,  All resident qualify. The IRS states: The June 17, 2024, deadline applies to individual income tax returns and payments normally due on April 15, 2024.

CA is following the federal so no payment is due yet.