Road bike vs. Mountain bike shoes
The majority of overshoes are designed to be worn with road specific shoes; these shoes have a smooth sole except for a heel pad and the cleat, therefore the overshoes can wrap around the sole allowing a close fitting profile. However, you can also buy overshoes that are suitable for mountain bike shoes as well; mountain bike shoes have lugs and studs on the sole, so these overshoes have a larger opening on the base to allow the tread to protrude. These kind of overshoes are also useful for commuting, where you may have to walk longer distances in your shoes, as they avoid you scuffing the fabric underneath the shoe when you walk.
If you are looking for overshoes that are suitable for mountain bike shoes as well as road cycling shoes, then consider those that have a Velcro fastening under the sole rather than just two openings at cleat and heel. The Velcro fastening is less likely to interfere with the tread on mountain biking and commuting shoes.