Simply put, something is biodegradable if it can be disintegrated by bacteria, fungi, or some other biological process of its own. Composting is the process of recycling organic waste so that it can eventually be reused, done under specific conditions (in industrial composting) where oxygen, heat and moisture are monitored.
The primary difference between compostable bio-plastics and biodegradable products is that industrially compostable products require a specific setting in order to break down, whereas biodegradable products break down naturally, in a similar way to how home compostables do. Typically composting is a faster process.