My interpretation as follows;-
Engine surge in relation to a jet/turbine is a fairly non technical word that can describe any type of undemanded, usually intermittent, power increase/decrease, possibly due to a faulty fuel control unit not regulating the fuel flow correctly. Occasionally, the word surge may be used in the event of a compressor stall. In my view this is an incorrect use of the word and may be misleading to an engineer trying to fix an engine problem
Compressor stall is when the flow of air through the compressor becomes unstable, the results of which will vary depending on the engine type and the severity of the stall. Typical symptoms can include a popping noise from the compressor or maybe a roaring noise. This can be accompanied by rising combustion chamber temperature and reduction in power. In severe cases, the engine can flame out or overtemp. Most modern engines are fairly reliable and will have devices fitted to minimise the chance of compressor stall. The typical helicopter engine consists of a multi stage axial compressor pumping air into a centrifugal compressor prior to the combustion chamber. This configuration does have problems as usually the axial compressor produces too much air for the centrifugal compressor at the lower rpm ranges. Manufacturers will usually fit a bleed valve between the two compressors which will be open at lower rpms to dump excess air. As the engine rpm increases, the valve will close allowing the total air flow into the centrifugal compressor.
Other causes of compressor stall are damaged or dirty compressor blades, recirculation of hot exhaust gases being sucked into the compressor when hovering downwind, FOD, incorrectly set up fuel control units, poor intake design etc, etc.
I'm sure there are very good written references which will describe surge and stall in much greater technical detail than I can but I hope this gives you some help.