These 2 types of insurance provide coverage for unique needs.
Critical illness pays you the benefit if you unfortunately acquire one of the illnesses covered in your policy. The big 3 are heart attack, cancer or a stroke. Depending upon the insurance carrier, there may be more illnesses covered. Coverage may also include some incremental programs, such as best doctors. Critical illness offers a one time payout. Why would this be useful? If you need to take extended time off work, it can serve to buffer your income. If you would like to invest in an experimental treatment in another country, this could help with those costs.
Disability insurance, on the other hand, is income replacement. If you are unable to work for an extended period, Disability will continue to pay you for an extended period. Most corporate benefits plans include a DI component, for at least a limited time (usually 2 years). If you are self employed and/or a professional, disability insurance will be crucial to your plan to ensure you can carry on living your life if the unfortunate were to happen from illness or accident.