There is no difference on (money supply) inflation between the federal government creating money through issue and the federal reserve creating money through issue. The difference is that by having the fed do it, we also incur interest costs, which would not be the case through direct issue.
A major difference is actions that could be undertaken if inflation takes off.
If the Treasury issued the money directly, there's nothing the Treasury can do.
If the Fed created the money, they can sell the bonds and extinguish the proceeds.
The difference is that by having the fed do it, we also incur interest costs
Which the Fed rebates, after minor expenses, to the Treasury.