The term 'supervisor' is usually used for the lower level management. For example, somebody who works alongside operational staff, but has some additional management responsibility. 'Manager' can be used for any level within the hierarchy, and usually denotes a person whose main, or only, function is management.
For example. A warehouse supervisor will work in the warehouse, often involved in the physical movement of stock, but also responsible for allocating tasks to other team members, carrying out administrative functions, and signing for deliveries. Warehouse staff report to the supervisor. A warehouse manager works in an office close to the warehouse, is responsible for higher-level tasks and probably has a number of supervisors reporting to him / her.
I hope this helps.