Deriving metallicities for solar-like stars follows well-established methods, but for cooler stars such as M dwarfs, the determination is much more complicated due to forests of molecular lines that are present. Several methods have been developed in recent years to determine accurate stellar parameters for these cool stars (Teff<4000K). However, significant differences can be found at times when comparing metallicities for the same star derived using different methods. In this work, we determine the effective temperatures, surface gravities, and metallicities of 18 well-studied M dwarfs observed with the CARMENES high-resolution spectrograph following different approaches, including synthetic spectral fitting, analysis of pseudo-equivalent widths, and machine learning. We analyzed the discrepancies in the derived stellar parameters, including metallicity, in several analysis runs. Our goal is to minimize these discrepancies and find stellar parameters that are more consistent with the literature values. We attempted to achieve this consistency by standardizing the most commonly used components, such as wavelength ranges, synthetic model spectra, continuum normalization methods, and stellar parameters. We conclude that although such modifications work quite well for hotter main-sequence stars, they do not improve the consistency in stellar parameters for M dwarfs, leading to mean deviations of around 50-200K in temperature and 0.1-0.3dex in metallicity. In particular, M dwarfs are much more complex and a standardization of the aforementioned components cannot be considered as a straightforward recipe for bringing consistency to the derived parameters. Further in-depth investigations of the employed methods would be necessary in order to identify and correct for the discrepancies that remain.