A Bridge and a Partial essentially serve the same function. They both replace missing teeth but one is removable and the other is permanently fixed.
A Partial is used to replace missing teeth on the same arch but can be used for one or both sides of your mouth. A successful partial needs a few natural teeth to grab onto to stay in place. It may be made with tissue colored resin or a combination of metal and resin.
A Bridge can also be used to replace a missing tooth or teeth in the same area of your mouth. It is designed to bridge the gap from one tooth to the next by anchoring a natural tooth on each side of the space. They can be made with various materials but typically a tooth colored bridge is chosen for aesthetics.