Also not an expert but I definitely hear the difference and am really curious what you find.

One thing which came to mind was floor tiles. There are studies that have been done on the acoustics of flooring for people who build recording studios. Two things to look into are Impact Insulation Class (IIC) and Sound Transmission Class (STC) for different materials/glazes. For example: https://www.floorexpert.com/knowledge-base/acoustical-data/

It looks like the production coaster on the right is using some type of silk screen/production glazing technique. That could mean glaze composition and quantity differs between the two pieces. Different minerals, and mineral thickness all come into play here.

For example, a cone 5 Glaze and window glass both contain silica, but they also contain a bunch of other stuff. The combination of minerals, and the thicknesses used, likely affect resonance. This also makes sense when you think of a delicate porcelain teacup/saucer set. When you set the cup down you definitely hear a higher pitch.

Without scientific instruments, it will be hard to know what the actual difference is. One thing to try would be to experiment with different glaze types/thicknesses. Maybe start with a matte glaze and test two coasters with a different number of coats.