Reason is thermal expansion. When materials are heated (by body heat, weather, etc), molecules move faster and occupy more space, causing material to expand. When materials are cooled (for example during winter, etc), molecules move slower and occupy less space, causing material to contract.
If there's no gap between the stone and the metal, the stone will crack because there's no space to expand to.
You can also see these gaps in train platforms, bridges, and other structures, to accommodate for expansion.
We also have to remember that:
1. Different materials/stones have different coefficients of thermal expansion (CTE), which means some materials may expand more than others. In general, mother-of-pearl is a composite (i.e. made of many materials) and therefore has a higher CTE than carnelian, which is a form of quartz (i.e. one material which is a crystal). So it's possible that your MOP doesn't have a big of a gap because it has expanded to the space allocated to it, than the carnelian.
2. These are made by hand so there may be variations in gap size from one creation to another, or between stones, or even between motifs