SDI is not Social Security. Social Security disability is often referred to as SSDI. SDI and SSDI are not the same thing. SDI is state disability insurance. The details are different for each state. But SDI is for short-term disability, usually only for 6 months. The Prudential plan is probably long-term disability, which is intended to pick up when the short-term state disability ends.
You should also apply for Social Security disability benefits. It might not take so long. Certain diseases and treatments, including certain types of cancer, get automatic approval without a long wait. The Prudential coverage is probably supposed to be only an add-on to what you get from Social Security. It probably requires you to apply for Social Security disability. When you get the Social Security payments you will then have to pay back Prudential for what you got from Social Security.
You should let your employer's HR department guide you through all of this. You should also call Social Security at 800-772-1213 to get information about it.
Social Security disability is taxed the same as Social Security retirement benefits (even if you are nowhere near retirement age). The amount that's taxable depends on your other income. Anywhere from zero to 85% of your Social Security benefits will be taxable. It's never fully taxable. If Social Security is your only income for the year, none of it is taxable.
