SSI stands for Supplemental security income while SSDI stands for Social Security Disability Insurance. Both these are government-operated programs that aim at helping disabled people financially, owing to the setback caused to their working abilities and earning potential due to their disabilities. Both these schemes should be looked into while divorcing a disabled person.
The major difference between both is that SSI is a need-based program and almost any disabled person can apply to it while SSDI streamlines its candidates by being a work-based program. SSDI aims at people with recent work experience.