Callable bonds fixed income

Hi,

If I have two bonds with a flat yield curve of 10%, which bond is the lower coupon bond and the higher coupon bond?
Lets say that bond a responds less to interest changes and bond b responds more hefty to interest changes. The coupon rates are 6% on one bond and 12% on the other.

I guess it is bond b that is the higher coupon bond since it responds heftier to interest changes right?

Duration is inversely related to the bond’s coupon rate

Yes so with greater coupon payments the lower duration because we receive higher cash flows in early periods. But I get confused here, like if we have change in interest rates, then should I think that the higher coupon bond gets less affected because the cash flows are being paid off quicker than the low coupon bond which have longer cash flow periods and therefore are more dependent on the interest rate?
Have I understood it correctly? Thanks!