Scanning ion conductance microscopy (SICM) is a nanopipette-based scanning probe microscopy technique that utilizes the ionic current flowing between an electrode inserted inside a nanopipette probe containing electrolyte solution and a second electrode placed in a bulk electrolyte bath, to provide information on a substrate of interest. For most applications to date, the composition and concentration of the electrolyte inside and outside the nanopipette is identical, but it is shown herein that it can be very beneficial to lift this restriction. In particular, an ionic concentration gradient at the end of the nanopipette, generates an ionic current with a greatly reduced electric field strength, with particular benefits for live cell imaging. This differential concentration mode of SICM (ΔC-SICM) also enhances surface charge measurements and provides a new way to carry out reaction mapping measurements at surfaces using the tip for simultaneous delivery and sensing of the reaction rate. Comprehensive finite element method (FEM) modeling has been undertaken to enhance understanding of SICM as an electrochemical cell and to enable the interpretation and optimization of experiments. It is shown that electroosmotic flow (EOF) has much more influence on the nanopipette response in the ΔC-SICM configuration compared to standard SICM modes. The general model presented advances previous treatments, and it provides a framework for quantitative SICM studies.