When you fill a bath, Is it different that you fill it directly or non-directly?
If the beaker is at or below the outlet of the faucet, the two values should be nearly identical.  There are very small effects, like water sticking to the outside of the beaker as it overflows or the surface of the water changing shape constantly (splashing out more at some times and less at others as a result.)  Those are insignificant for practical purposes.

If the top of the beaker is above the outlet of the faucet, that is, the faucet is submerged in the beaker, then there will be a small addition to the height to which the water must be pumped.  It's only centimeters, but the pressure increase and flow decrease is entirely measurable and would have a small but significant and predictable effect over the course of running a bath.