Pulse means the overload of large power and with long duration(large energy) whereas surge means overload like ESD, of high voltage and with short duration. Anti-pulse resistors are unlikely to be damaged even if large power is instantaneously applied.
Among SMD type resistors, thick film chip resistors, like compact Microhm NBS Series, are generally stronger against pulse than metal film chip resistors. Thick film chip resistors with special construction are strong against pulse or surge. Metal plate chip resistors for current sensing apply metal plate for resistive body. This achieves the strong resistance against pulse or surge.