Feeders are the aggregate circuit that serves a distribution device (panelboard, load center) containing multiple branch circuits. Feeders connect subpanels from the main panel, or the main panel from the service equipment.
Branch circuits connect the branch overcurrent device (e.g. branch breaker) to each load. Or to a daisy-chained group of loads, as is the case with receptacle and lighting circuits. The way to tell that it is a branch circuit, is that it will not have multiple paralleled overcurrent devices on the load side of the circuit.
In both cases, you can de-energize the feeders and branch circuits with customer-owned disconnects. Service conductors come ahead of feeders, ahead of the main service disconnect, with the essential difference being that you need the utility to shut down your service, to de-energize them.