Biodgradable means that it can be broken down by a biological agent, however most people assume it means that it will break down under normal conditions or "in the wild" which is not the case.
Composting is a controlled process, regardless of whether it's your backyard or an industrial facility, where the materials undergo exposure to certain conditions that expedite, or in the case of PLA, facilitate decomposition.
Compostable is a subset of biodegradable, is there a term for biodegradable items that will decompose under uncontrolled conditions?
To me "compost" is a decomposing pile of natural materials. Plants, certain types of food waste, animal waste, etc. that anyone can put in their backyard (or scale up to industrial size) to turn waste into nutrient rich soil.
A very specific industrial process that can break down a very specific type of material in just the right circumstances is so completely different that it seems odd to me to share the same name.