In a loop you can start from any point and return to that same point. A loop is the same thing as a complete circuit. A branch is a piece of a loop. It has distinct endpoints. It is not a complete circuit.
The term "branch" is also used in building wiring - refers to wiring from a given breaker in a panel. "Loop" is not used in this context, though. "Feeder" is the circuit that feeds the panel - coming from a more robust breaker panel if in larger building. "Service" is what powers the feeders.
"Loop" is also used in fire alarm systems. Definition is similar to that given by Papabravo above.
"Service Loop" is a coil of extra conductor in a circuit. It is stored for the convenience of service personell.