While the effects may be similar, they are fundamentally different mechanisms.
Also, this statement is incorrect:
> Simplified: the central bank decide on an interest rate that they want to see. By itself that decision doesn't do anything.
The Fed does in fact set interest rates and that decision directly impacts rates all down the line to mortgages and local loans. Intervening in the bond market is another tool that the Fed can use.
The Fed still has to make (and receive) loans at these rates, for them to have an effect on the market.
I think you're talking past each other.
A central bank doesn't directly set interest rates for your mortgage.
It can set rates at which it will lend to other banks, which in turn influences the rates banks will offer to mortgage borrowers, but this isn't necessarily so, see for example 2008.
Of course there are more contracts directly tied to the central bank rates, but thats just formalising the thing thats supposed to happen anyway.
Yes. Btw, I'm not sure how many contracts are directly tied to whatever rate the central bank announces these days? It used to be more common to tie contracts to eg LIBOR, which is or was a reported interbank lending rate, not a decreed one.