  Elemental abundances of Sun-like stars are crucial for understanding the
detailed properties of their planets. However, measuring elemental abundances
in M stars is challenging due to their faintness and pervasive molecular
features in optical spectra. To address this, elemental abundances of Sun-like
stars have been proposed to constrain those of M stars by scaling [X/H] with
measured [Fe/H]. This study tests the robustness of this practice using M- and
GK-dwarf stellar abundances and rigorous statistical methods. We compile
elemental abundances for 43 M dwarfs for 10 major rock-forming elements (Fe, C,
O, Mg, Si, Al, Ca, Na, Ni, and Ti) from high-resolution near-infrared stellar
surveys. We perform bootstrap-based linear regressions on the M dwarfs to
determine the trends of [X/H] vs. [Fe/H] and compare them with GK dwarfs. A
2-sample, multivariate Mahalanobis Distance test is applied to assess the
significance of differences in [X/H]--[Fe/H] trends for individual elemental
pairs between M and GK dwarfs. The null hypothesis of no significant difference
in chemical trends between M and GK dwarfs is strongly rejected for all
elements except Si, for which rejection is marginal, and Na and Ni, for which
results are inconclusive. This suggests that assuming no difference may lead to
biased results and inaccurate constraints on rocky planets around M dwarfs.
Therefore, it is crucial for both the stellar and exoplanet communities to
recognise these differences. To better understand these differences, we
advocate for dedicated modelling techniques for M dwarf atmospheres and more
homogeneous abundance analyses. Our statistically constrained trends of
[X/H]--[Fe/H] for M dwarfs offer a new constraint on estimating M-dwarf
elemental abundances given measured [Fe/H], aiding in characterising the
properties of M dwarf-hosted rocky worlds.
