If you try to block with your finger the flow of the water out of the faucet or a water hose, the water's speed increases. But while you're blocking the water flow out of the faucet by turning the handle, the speed doesn't increase. So what's the difference between the two ?
In both cases (covering with thumb and turning handle), the volumetric flow rate decreases. The flow rate is proportional to the 4th power of orifice diameter, in accordance with the Hagen–Poiseuille equation. The velocity is greatest at the smallest cross section in both cases, but you can not see the smallest cross section in the facuet, the way you can when you cover the end of hose with your thumb. Downstream of the smallest cross section in the facuet, the cross section increases, so the velocity slows before the water comes out.