Double diffusion encoding (DDE) makes diffusion MRI sensitive to a wide range of microstructural features, and the acquired data can be analysed using different approaches. Correlation tensor imaging (CTI) uses DDE to resolve three components of the diffusional kurtosis: isotropic, anisotropic, and microscopic kurtosis. The microscopic kurtosis is estimated from the contrast between single diffusion encoding (SDE) and parallel DDE signals at the same b-value. Another approach is multi-Gaussian exchange (MGE), which employs DDE to measure exchange. Sensitivity to exchange is obtained by contrasting SDE and DDE signals at the same b-value. CTI and MGE exploit the same signal contrast to quantify microscopic kurtosis and exchange, and this study investigates the interplay between these two quantities. We perform Monte Carlo simulations in different geometries with varying levels of exchange and study the behaviour of the parameters from CTI and MGE. We conclude that microscopic kurtosis from CTI is sensitive to the exchange rate and that intercompartmental exchange and the transient kurtosis of individual compartments are distinct sources of microscopic kurtosis. In an attempt to disentangle these two sources, we propose a heuristic signal representation referred to as tMGE (MGE incorporating transient kurtosis) that accounts for both effects by exploiting the distinct signatures of exchange and transient kurtosis with varying mixing time: exchange causes a slow dependence of the signal on mixing time while transient kurtosis arguably has a much faster dependence. We find that applying tMGE to data acquired with multiple mixing times for both parallel and orthogonal DDE may enable estimation of the exchange rate as well as isotropic, anisotropic, and transient kurtosis.