See if this helps? http://www.ssa.gov/pubs/EN-05-11125.pdf

Social Security Disability Insurance (SSDI) is Social Security and based on your work history and how much you have paid into Social Security from your payroll checks so you probably do not qualify. SSI is Supplemental Security Income and while administered by Social Security, the money comes from elsewhere. But there is only one form to fill out and they see if you qualify for either/any.