The gradients of the mixture fraction and the reaction progress variable (or equivalently their scalar dissipation rates) play a major role in flamelet theory. Therefore, having appropriate closure strategies for these quantities is of vital importance for the applicability of the corresponding flamelet equations. While analytical closure expressions exist in some simple cases, the direct consideration of an equation in composition space is a much more general approach applicable to arbitrarily complex flames. However, in the last decades it has been shown that scalar gradient composition space equations with and without a temporal derivative can be formulated, which additionally make use of different definitions of the strain rate. Based on this spectrum of possibilities, the following important questions are raised in this work: 1) What is the general relation between the different definitions of strain and the transient evolution of scalar gradients? 2) Are both possible formulations of the scalar gradient equation capable of fully capturing unsteady effects? 3) What are the advantages and disadvantages of each formulation in the context of a full description of the flame structure evolution in composition space? To address these questions, a formal mathematical expression connecting the temporal derivative of the gradient of a generic scalar and two definitions of strain widely adopted in the literature is derived and examined. This relation is then discussed for a premixed flamelet with the progress variable as composition space coordinate and it is used to show the equivalence between the different versions of the corresponding gradient equation. Finally, the capabilities and limitations of each formulation are analyzed in the context of the extinction process of a lean planar premixed counterflow flame subject to an oscillating boundary condition for the flow velocity, where special emphasis is given to their advantages and disadvantages.