Detailed numerical calculations based on the solution of the full transport equations have been compared with flamelet calculations in order to analyse the flamelet concept for laminar diffusion flames. The goal of this work is to study the interactive (Lagrangian Flamelet Model and Interactive Steady Flamelet Model), and non-interactive (Steady Flamelet Model and Enthalpy Defect Flamelet Model) flamelet models considering both differential diffusion and non-differential diffusion situations, and adiabatic and nonadiabatic conditions. Moreover, a new procedure has been employed to obtain enthalpy defects in the flamelet library, the application of which has been found to be encouraging. The effect of using insitu, local or stoichiometric scalar dissipation rate conditions, and also the effect of using local or stoichiometric conditions to evaluate the flamelet-like time has been analysed. To improve slow species predictions using the non-interactive models, their transport equations are solved with the reaction terms calculated from the flamelet library, also considering local or stoichiometric conditions in the so-called Extended Flamelet Models.