A DSP and a CNA are different jobs that sometimes get written into the same wage bill. DSP means direct support professional: someone paid to support a person with an intellectual or developmental disability in community life. CNA means certified nursing assistant, a credential issued through a state's nurse aide registry. The CNA works under nursing rules, often in a nursing facility, a hospital, or home health.
The overlap is the tasks. Both jobs can include bathing, dressing, meals, and mobility. That is why a statute aimed at "caregivers" or "direct care" can sweep them together. The training, the license, the supervisor, and the payer are not the same. A CNA has completed a state-approved nurse aide program and is on a registry. A direct support professional is not required to hold that credential. Some people hold both. Most do not.
Where the work happens is the other split. CNA work is organized around nursing and facilities. Direct support is organized around a waiver, a group home, a person's own apartment, or a day program. A nursing facility and an ICF/IID are both institutions, and they are still different benefits with different staff rules. A waiver group home is neither one.
Pay comparisons that treat the jobs as substitutes miss the rate. A CNA wage is often tied to a nursing facility or home-health rate. A DSP wage is tied to a disability provider's fee schedule, which may include a wage floor that moves on its own schedule. An agency that employs both titles has two sets of rules, not one blended job.
Use DSP when the story is community disability support. Use CNA when the story is nurse-aide certification. Use direct care worker only when the document itself chose the umbrella, and then say who it included.