  We show, both analytically and numerically, that non-Gaussian tails in the
probability density function of curvature perturbations arise in
ultra-slow-roll inflation from the $\delta N$ formalism, without invoking
stochastic inflation. Previously reported discrepancies between both approaches
are a consequence of not correctly accounting for momentum perturbations. Once
they are taken into account, both approaches agree to an excellent degree. The
shape of the tail depends strongly on the phase space of inflation.
