Distance calculations and [M/H]/[Fe/H] values

Hello everyone! I am a high school student (senior), and an extremely beginner astronomer, but I am attempting to write a paper. Last year, my supervisors and I started observing the HU CAS variable star, got some good images, and plotted light curves.
At the moment, I am authoring the paper on the ability to apply the infrared period-luminosity relations to a variable star to determine the distance to the star. However, my calculations of the distance to the star don’t match the Gaia database nor the ASAS-SN data (and those two don’t match each other either). I have tried including/not including the interstellar reddening, and changing values (while still trying to understand the concept behind the logZ value).
I also don’t understand the difference between [M/H] and the [Fe/H] values as they seem to have different meanings on Gaia and ASAS-SN. Could someone please help me understand what is wrong or what I am missing? I can provide additional information if needed.

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This should add to the confusion or maybe yield some answers. .
https://www.sdss4.org/dr17/irspec/parameters/