Medicare pays first, always
Medicare is the primary payer for a person who has both. It processes the claim, pays what it covers, and only then does Medicaid consider the remainder. That is why a provider needs both cards, and why a claim that was never sent to Medicare will not be picked up by Medicaid later without a fight.
What Medicaid picks up depends on the level of eligibility. People with full Medicaid have their Medicare premiums and cost sharing covered almost entirely. People in a Medicare Savings Program have narrower help, usually the Part B premium and some cost sharing. The label on the letter matters more than the fact of being enrolled.
