Stall verses Surge
To expand on A33Zab's post: A stall (rotating stall) is a flow breakdown at one or more compressor blades. A rotating stall is a stagnated region of air which moves in the circumferential direction of rotor rotation, but at a fraction of the rotor speed. At a given throttle setting it does not move axially in either direction although pressure waves may be created that move upstream (compression waves) or downstream (rarefaction waves). There are two types of stalls. Blade stall is a two-dimensional type of stall where a significant portion of the blade has large wakes due to separation of the suction surface boundary layer (convex side of the blade). The other stall is an end-wall boundary layer separation. In either case the sound would be a single "bang".
Surge is a response of the entire engine which is characterized by a flow stoppage or reversal in the compression system. Upon surge, a compression component will unload by permitting the compressed air in downstream stages to expand in the upstream direction forming a planar wave which at high rotational speeds leads to flow reversal. The compressor can recover and can begin to pump flow, however if the cause of the surge is not removed, the compressor will surge again and will continue to surge/recover until some relief is provided. A surge can be initiated by a rotating stall. In this case, the sound would be a series of "bangs" with noticeable flames coming out of the engine. Surges can be very damaging to the compressor system.
For a given compressor, one can construct a performance map given developed data. On the vertical axis would be total pressure ratio, and on the horizontal axis would be corrected compressor inlet airflow. A stall line is constructed above the engine operating line. At low inlet airflow, the lines are very close to each other, but diverge as total pressure ratio and inlet airflow increases, e.g., takeoff, max climb and max cruise. So there is more stall margin designed into a compressor at critical speed operational points verses typical ground operations.