Yes, you can receive both, FERS Disability Retirement and Social Security Disability Insurance (SSDI). Social Security has a much stricter definition for "disability".
If your approved for SSDI, there is an offset for FERS Disability Retirement. Look at it as two jobs; but, your boss at one is not happy about the second job and reduces your pay! You still receive two pay checks.
Also, with annuity payment, you get paid once a month rather than bi-weekly.
During the first year FERS Disability Retirement's annuity is 60% of your high-3; but, 100% of any SSDI that you receive is deducted from your OPM/FERS Disability Retirement annity. The second year you received 40% of your high-3; but, 60% of any SSDI that you receive is deducted from your FERS Disability Retirement annity.
What I did not know is any COLA that you receive from Social Security IS NOT recaucu... for the 60% offset.
In regard to the FERS Disability Retirement COLA, if the COLA in any given year is greater that 2%, it is 1% less than the CSRS COLA. This year the Social Securty and CSRS COLA was 5.8%. The FERS COLA was 4.8%.
Hope this answers your question.