Illness benefit (IB) and disability benefit (DB) are the same thing - IB used to be called DB up to a couple of years ago.
From IB, if you are medically eligible you can transfer to Invalidity Pension (if you've got sufficient PRSI contributions) or Disability Allowance (which is means-tested).
Have a look at www.welfare.ie and follow the link "a person with a disability or illness" for all of your options & entitlements.