When I use Path/Difference, the produced object seems to change it's shape a bit, I think it becomes a bit thinner for some reason, meaning that it does not sit flush with the original object. Specifically, I noticed this when I attempted to "Difference" 2 circles, one bigger one smaller. I needed the resulting quarter moon shape to be aligned with the original smaller circle, but instead it thinned out a bit, resulting in the circle sticking out on the sides... anybody got any advice on how to fix it?

What you're seeing might be either a known problem or related to one. But it's hard to say without seeing the SVG file. Can you share it?

I hesitate to elaborate until we I can confirm it's the same problem I'm thinking of.

Can you check if they all have the same stroke width?