If we look at plastics, those marked with numbers 1 and 2 can be recycled. Most so called biodegradable garbage bags are made up of plastic number 7 and hence cannot be recylced. The degreet to which the material degrades in nature is dependent upon the amount of surface area of the bag that is exposed to mositure, light and air ( the natural elements).
The other arguement is that methane gas release in the process is more harmful than carbon di oxide. If we have a backyard compost unit, then the temperature generated would not be high enough for the biodegradable bags to breakdown.
Although both terms are used interchangably, there is a difference and most enviornment consious people go for the compostable bag.
The compostable bags are made up of a unique plastic material that is broken down by a bacterial enzyme into carbon dioxide, biomass and water. The material and the manufacturer should meet the EN 13432 guidelines. This speaks about the amount of chemicals, and the time limit ( 90% of the material should be broken down physically by 3 months and chemically by 6 months). Some companies produce compostable bags that are made up of cornstarch and potato starch. These bags can be used for self generated kitchen waste and be used in the backyard or small community based compost units without much chance of the harmful regular plastic entering the system.
So, in simple terms, going for a compostable garbage bags would be more safer that going for a biodegradable bag.