I have been involved with Social Security for about thirty years, between actually working for the agency and being an attorney, and I have never heard the term "preferred SSI". It does not exist!
SSI (Supplemental Security Income) and SSD (Social Security Disability) are both programs run by Social Security. The same medical requirement is in place for both, the inability to do any type of substantial work for at least a year. The non-medical part is the difference. SSI is a needs based program, which means you have to have limited (or no) income and resources. SSD requires someone to work and pay into Social Security for a certain amount of time, with the added requirement that the work be recent. For most people this means work for five years total in the last ten years. There is no requirement to have low income or assets. Some people qualify for one program, some qualify for the other, some for both, and, unfortunately, some for neither program. Social Security can tell you quickly if you qualify non medically. The medical decision takes some time for a deciision.