The laser-induced damage threshold (LIDT) of optical components is one of the major constraints in developing high-power ultrafast laser systems. Multi-layer dielectric (MLD) coatings-based optical components are key parts of high-power laser systems because of their high damage resistance. Therefore, understanding and characterizing the laser-induced damage of MLD coatings are of paramount importance for developing ultrahigh-intensity laser systems. In this article, we overview the possible femtosecond laser damage mechanisms through damage morphologies in various MLD optical coatings tested in our facility. To evaluate the major contributions to the coating failure, different LIDT test methods (R-on-1, ISO S-on-1 and Raster Scan) were carried out for a high reflective hybrid Ta2O5/HfO2/SiO2 MLD mirror coating at a pulse duration of 37 fs. Different LIDT test methods were compared due to the fact that each test method exposes the different underlying damage mechanisms. For instance, the ISO S-on-1 test at a higher number of laser pulses can bring out the fatigue effects, whereas the Raster Scan method can reveal the non-uniform defect clusters in the optical coating. The measured LIDT values on the sample surface for the tested coating in three test methods are 1.1 J/cm2 (R-on-1), 0.9 J/cm2 (100k-on-1) and 0.6 J/cm2 (Raster Scan) at an angle of incidence of 45 deg. The presented results reveal that the performance of the tested sample is limited by coating defects rather than fatigue effects. Hence, the Raster Scan method is found to be most accurate for the tested coating in evaluating the damage threshold for practical applications. Importantly, this study demonstrates that the testing of different LIDT test protocols is necessary in femtosecond regime to assess the key mechanisms to the coating failure.