It is shown that, if $f$ is a meromorphic function of order zero and $q\in\mathbb{C}$, then
\begin{equation}
\label{abstid} m\bigg(r,\frac{f(qz)}{f(z)}\bigg)=o(T(r,f))
\tag{\ddag}
\end{equation}
for all $r$ on a set of logarithmic density $1$. The remainder of the paper consists of applications of identity \eqref{abstid} to the study of value distribution of zero-order meromorphic functions, and, in particular, zero-order meromorphic solutions of $q$-difference equations. The results obtained include $q$-shift analogues of the second main theorem of Nevanlinna theory, Picard's theorem, and Clunie and Mohon'ko lemmas.