It appears you are on a State Plan that is an Advantage Plan and not a Supplement Plan.
It appears you are in a State Advantage Plan and chose not to be insured with the Original Medicare Plan and it appears that is why you do not need to show your Original Medicare Plan Card.
Those of us on a State Plan in OK can be on the Original Medicare Plan they choose and have the Supplement Plan at the same time or they can be on the State Advantage Plan and no longer have the Original Medicare Plan coverage. In other words the Supplement Plan keeps you in the Original Medicare Plan of your choice ( I have plan G). The Supplement with the Original Medicare Plan works together. The Original Medicare Plan as the primary plan and the Supplement plan as the secondary plan. One of the big differences is who gets to chose where you can go for medical help and who you can see as a doctor, hospital or clinic etc.
The Original Medicare Plan allows you to go anywhere. to see any medical professional in the US that accepts Medicare and in many cases you don't need referrals from a primary doctor if you want to see a specialist. Generally one of the other big differences that usually comes into play is the costs of a hospitalization and the deductible costs for the hospital stay.
There is so much to really understand when it comes to insurance, as we know.
The costs, as with almost everything, of insurance plans are also a big factor when it comes to deciding.
Hope this and Sue's reply has helped anyone who needs to decide at age 65 when it is time for Medicare sign up.
Barbara