The payments you are receiving from the State of California EDD are known as California State Disability Insurance or SDI benefits. You may only receive these benefits for 12 months. The federal Social Security disability benefits you have applied for are paid by the U.S. federal government from the Social Security trust fund if you qualify for Title II Disability Retirement Insurance benefits or if you do not have a sufficient work credits to qualify for the the Title II Program, then you may qualify for Social Security Supplemental Security Income or SSI Title XVI benefits.
If you have been approved for SSDI benefits, you may still receive EDD benefits, but your federal disability benefits may be reduced somewhat.
I recommend that you meet with EDD and SSA staff to confirm your disability status with both agencies and your sources of income. If either agency charges you with an overpayment, you may be able to request a waiver if you timely reported receiving the income from each source.
Review the information at the SSA website as this may also be helpful to you.
This advice is not a substitute for a thorough evaluation of all of the facts of your case by a disability benefits advocate or attorney