What Perna says is how I understand it as well.
Just to offer the same info but in a story form, I'll tell you what happened when I was on disability.

When I was on disability I had SSI and SSDI.
I had SSDI because I had worked enough quarters to qualify for Social Security.
But my SSDI benefits were less than my States SSI benefit so I also received an SSI benefit.
I received both benefits via direct deposit, they were deposited separately into my bank account.
After 2 years on disability I qualified for Medicare. Originally I had Medicaid. Because of my low income (actually no income but you can have some) I had Medi/Medi or both but my primary was Medicare. This was a good thing because Medicare is much better than Medicaid.

I'm not sure how they did the calculations but I received more in benefits (only about $20 but one could receive hundreds more a month) because I had SSDI. You won't receive less, hopefully more, maybe the same as SSI only.

This IS a good thing!!!

It really frustrates me how confusing gov stuff is, it seems unnecessarily confusing. You're not alone trying to decipher this wacky system. Sorry it's so stressful. I'm happy for you tho because SSDI is much better.