States Achieve Medicaid Expansion Act of 2021 or the SAME Act of 2021 This bill provides an enhanced federal matching rate to every state that expands Medicaid coverage for individuals who are newly eligible under the Patient Protection and Affordable Care Act, regardless of when such expansion takes place. Under current law, the enhanced Federal Medical Assistance Percentage (FMAP) is equivalent to 100% in 2014 through 2016, 95% in 2017, 94% in 2018, 93% in 2019, and 90% thereafter. The bill retains this enhanced FMAP, but bases it on a term of years rather than on specific dates. The bill applies retroactively.