You must apply for Social Security Disability alongside your Federal Disability Retirement application; however, it is not required that you are approved for SSDI to be eligible for Federal Disability Retirement. If you are approved for both benefits, Social Security will become the primary source of income and the two benefits will offset.

During the first year you are receiving the benefits simultaneously, your Federal Disability Retirement annuity will be reduced by 100% of your Social Security Disability payment.

The second year and beyond, your disability retirement annuity will be reduced by 60% of your Social Security Disability payment.

As you can see, after the first year you will have the potential to receive more income than if you had just been on one of these benefits.

Social Security Disability: https://www.federaldisability.com/leg...
Federal Disability Retirement: https://www.federaldisability.com/leg...