Changing the variance value will change the duration of the elementary function (window size), and the center of the elementary function is no longer fixed.
At weak decay of the self-pulsation (even in the case of strong spiking), the solution of corresponding equation can be approximated through elementary function.
For this reason, people will often distinguish the meanings of the two terms in this context, using image for the abstract categorical concept and range for the elementary function-theoretic concept.