Open market operations are the mechanism by which the interest rate is controlled.
Basically, the central bank sets an interest rate target and then performs open market operations until the interest rate matches the target.
That obviously affects the quantity, but the point is that the target is the interest rate. The quantity just ends up being whatever happens to be necessary to hit the interest rate.
The target is inflation in both.
When you reduce the volume of assets available, or the price renting the asset, you increase it's value. In this case the asset is money.
Market interest rate is a signal how effective the action is long before inflation statistics is available.