Still perplexed about Medicaid and Medicare...

My mom has dual Medicare/Medicaid coverage now. In Michigan there is a Medicaid Waiver program, which she qualifies for. She has in-home aides come to her house 2x a day for 5 hours total each day, 7 days a week, to help with cooking, cleaning, errands, and just plain companionship. Plus she has a weekly nurse visit, where the nurse takes her vitals and fills her pill box. The pill box she has is paid for thru the Waiver, as it is a locked/alarmed pill box, and she has a Life Alert pendant and pull-ups/bed pads all paid thru Medicaid Waiver.

Some programs - like PACE or other community based programs- require for the elder to be a “dual”, that is on both Medicare AND Medicaid. As between the billing to each M&M, the costs of the program is covered.

Often community programs cannot deal with taking self pay or non M&M payment systems as everything has to fit a Medicare or Medicaid code.

If you have Medicare, it becomes your primary insurance. Medicare covers hospital stays under part A, not long-term residential care. It covers rehab at varying rates depending on length of time and progress for recovery. Medicare has a part D that has various plans that cover drugs at different rates.
Medicaid is a state run program that uses both state and federal dollars. It has federal oversight in some ways but Barb, EVERY state administers its care differently.
New York's in home caregivers 24/7 is unique to NY. Part of the reason that is offered in NY has to do with a lack of facilities and inability to build new facilities to house the population in the densely populated with no new real estate location. There is no way in heck you'd get that in Texas. For the same reason you don't get individual care at day care, individual teacher at preschool or school, you won't get 24/7 1:1 attention with Medicaid. It's not cost-effective. 24/7 care is 8,760 hours per year. That is $131,400 ($360 daily rate at a caregiver rate of $15/hour which is LOW for the US) for 1:1 care that doesn't have trained, certified nurses and other medical staff in the same building or assistance for 2 person lifts or back-up in case of illness or vacation. Online research yields this result:
Below are some national average costs for long-term care in the United States (in 2016). Average costs for specific states are also available.
Texas nursing homes average $4000-$6000 per month. The 24/7 model above would cost at least $10,950 in 1:1. Communal living is almost always cheaper for a state agency to provide care as the costs are shared.
$225 a day or $6,844 per month for a semi-private room in a nursing home
$253 a day or $7,698 per month for a private room in a nursing home
$119 a day or $3,628 per month for care in an assisted living facility (for a one-bedroom unit)
$20.50 an hour for a health aide
$20 an hour for homemaker services
$68 per day for services in an adult day health care center

Found by searching google
"Medicare and Medicaid are two different government-run programs that were created in 1965 in response to the inability of older and low-income Americans to buy private health insurance. They were part of President Lyndon Johnson’s “Great Society” vision of a general social commitment to meeting individual health care needs. Medicare and Medicaid are social insurance programs that allow the financial burdens of illness to be shared among healthy and sick individuals, and affluent and low-income families.
Medicaid is not the same as Medicare.
Medicare is a federal program that provides health coverage if you are 65 or older or have a severe disability, no matter your income.
Medicaid is a state and federal program that provides health coverage if you have a very low income.
If you are eligible for both Medicare and Medicaid (dual eligible), you can have both. Medicare and Medicaid will work together to provide you with very good health coverage.

Who are the people you are talking to, WS?

It may vary by State. I live in NYC. People here can get 24/7 home attendent care, paid for by Community Medicaid, which differs from Nursing Home Medicaid. Then, there are Medicaid Waivers, which allow folks to stay at home with "patient directed care" meaning that they can chose to have a family member be their caregiver and get paid for it.

I believe, especially if you are a Community Spouse (the spouse who does NOT need care) that a certified Elder Care attorney needs to be consulted about these issues.

Anyone over 65 has Medicare, and I believe that that is primary for hospitalizations. medicaid would pay for doctor visits, medications and the like.