  We examine in detail the relationship between smooth fast quantum quenches,
characterized by a time scale $\delta t$, and {\em instantaneous quenches},
within the framework of exactly solvable mass quenches in free scalar field
theory. Our earlier studies \cite{dgm1,dgm2} highlighted that the two protocols
remain distinct in the limit $\delta t \rightarrow 0$ because of the relation
of the quench rate to the UV cut-off, i.e., $1/\delta t\ll\Lambda$ always holds
in the fast smooth quenches while $1/\delta t\sim\Lambda$ for instantaneous
quenches. Here we study UV finite quantities like correlators at finite spatial
distances and the excess energy produced above the final ground state energy.
We show that at late times and large distances (compared to the quench time
scale) the smooth quench correlator approaches that for the instantaneous
quench. At early times, we find that for small spatial separation and small
$\delta t$, the correlator scales universally with $\delta t$, exactly as in
the scaling of renormalized one point functions found in earlier work. At
larger separation, the dependence on $\delta t$ drops out. The excess energy
density is finite (for finite $m\delta t$) and scales in a universal fashion
for all $d$. However, the scaling behaviour produces a divergent result in the
limit $m\delta t \rightarrow 0$ for $d\ge4$, just as in an instantaneous
quench, where it is UV divergent for $d \geq 4$. We argue that similar results
hold for arbitrary interacting theories: the excess energy density produced is
expected to diverge for scaling dimensions $\Delta > d/2$.
