The term "metal" arises in astronomy since almost all the prominent lines in a stellar spectrum arise from metals like Na, Mg, Ca, Fe. In fact, when one looks in enough detail one can also find lines of C, N, O, F etc., but the term has stuck for anything heavier than He.
When measuring "metallicity", what is often being done is to estimate the abundance of Fe, since that element has lots of lines in the visible spectrum of most stars. However, these days, no astronomer that knows anything about stellar and Galactic evolution just assumes that the abundance of iron equates to the overall metallicity.
Very often, particularly with high quality, high resolution spectra, the abundances of many elements can and are measured individually. This is important because the predominant origins of the various elements are different - Mg is mostly produced in core-collapse supernovae, Ni and Fe mostly in type Ia supernovae, Sr can be produced in AGB stars etc. This means that these elements are enriched at different rates in the interstellar medium, because their progenitors have very different lifetimes. Thus, although very old stars are metal-poor, they are comparatively Mg-rich because Mg is produced faster in massive stars that then explode as supernovae on short timescales, than elements like Fe and Ni, which arise from type Ia supernovae with long-lived white dwarf progenitors (e.g. Bensby et al. 2005; Gonzalez et al. 2011)
It is also important because the abundance of different elements have different effects on the interior structure and evolution of stars - e.g. oxygen is a dominant opacity source at high temperatures.
Now, in practice, once you start looking at stars at the Sun's age and below, the differences in the abundance mixture for most elements are comparatively small (at the levels of <25% when compared to the abundance of Fe; Bensby et al. 2014). That is because the epoch of vigorous high-mass star formation has ceased and the products of individual events like supernovae are quickly mixed and diluted. Nevertheless, some individual elements still show interesting variations - Li is burned inside stars, but produced in Novae. This leads to fascinating abundance variations that are both a function of age and mass that are poorly correlated with overall metallicity. Individual s-process elements are comparatively rare, but their abundance continues to increase with time as they are produced by AGB stars, leading to an empirical stellar chronometer.
In summary: for most stars in the Galactic disk, the abundance mixture is reasonably close to that of the Sun. However, when we look closely at older stars or at particular elements, we see a much more complex picture and can use this to probe the history of star formation and the fine details of stellar evolution. Whilst models of "young stars" (stars born in the last few billion years) generally just use a solar abundance mixture along with a variable overall metallicity (because no great variations are observed in elements that would cause structural differences), there are many models out there featuring "alpha-enhancements" that increase the abundance of "alpha elements" (O, Mg, Si etc.) with respect to the iron-peak elements to simulate what happens in the early history of our Galaxy (e.g. Fu et al. 2018, Pietrinferni et al. 2020).