Medicare is a system by which (currently, a subset) of Americans may select[0] either publicly subsidized private health plans or a purely-public[1] option.

The difference between this and the ACA plus a public option is...not that much.

[0] well, except for many Medicare/Medicaid dual-eligibles, for which a single plan (often fully-publicly-subsized private) covering both programs is selected for them by their state.

[1] actually administered by regional private contractors under federal rules.