A rose by another name, right?

Medicare, as it exists today, is a single-payer medical care program, funded by the U.S. government. The government insures all seniors, guaranteed, and pays all major medical bills. Republicans, led by Paul Ryan, want to replace this with a voucher system, where you get a voucher and have to go buy private insurance. Oh, and the voucher doesn't keep pace with inflation, nor is there a guarantee it will cover your insurance costs.

We can replace Medicare with any kind of program we like, no matter how different, but as long as we call it Medicare, we're not ending it? That's what Politifact, among others, is claiming.

If you inherit the hatchet George Washington used to cut down the cherry tree, and you replace the head one year and the handle the next, do you still get to call it Washington's hatchet?