I applied for SSI only. Got it. Had it for 4 years and worked parttime and had enough credits finally for SSDI in Oct. 2011. However, for some reason they denied me the SSDI while still giving me the SSI. I appealed and won at judge level. Will I get SSDI back pay from Oct. 2011 to date or did SSI take it all? (I received my SSI back pay long ago.)

What did the judge say? Is there an administrative court order stating the terms?

Otherwise, call the involved agencies and ask. I do know that generally you cannot receive both disability and social security at the same time - one or the other. So if you were getting one, and later were approved for the other, they'd probably just transfer you from one program to the other, not pay you both for any simultaneous period. Is that what you're asking?