HHS.gov: U.S. Department of Health & Human Services
この説明を見つけて、すっきり整理できました。中絶で関係してくるのはメディケイドで、州ごとに扱いが違うのもそういうだったのですね。以下に原文と仮訳を示します。
What is the difference between Medicare and Medicaid?
Medicare
Medicare is an insurance program. Medical bills are paid from trust funds which those covered have paid into. It serves people over 65 primarily, whatever their income; and serves younger disabled people and dialysis patients. Patients pay part of costs through deductibles for hospital and other costs. Small monthly premiums are required for non-hospital coverage. Medicare is a federal program. It is basically the same everywhere in the United States and is run by the Centers for Medicare & Medicaid Services, an agency of the federal government.
For more information regarding Medicare and its components, please go to http://www.medicare.gov.
Medicaid
Medicaid is an assistance program. It serves low-income people of every age. Patients usually pay no part of costs for covered medical expenses. A small co-payment is sometimes required. Medicaid is a federal-state program. It varies from state to state. It is run by state and local governments within federal guidelines. To see if you qualify for your state's Medicaid (or Children's Health Insurance) program, see: https://www.healthcare.gov/medicaid-chip/eligibility/
For more information on Medicaid, please go to http://www.medicaid.gov