Referring to one manufacturer's nomenclature and systems:
The "AIRSPEED LOW" caution occurs shortly after the speed drops below the Minimum maneuver speed. The Min Maneuv spd is ~30% above stalling speed for slat/flap config. Even if the auto-throttle is not engaged in any mode, as long as the auto-throttle is armed, this is the speed at which "auto-throttle wake-up" takes place, ie the auto-throttle pushes the thrust levers up so as to regain speed without any pilot action. At typical weights and maneuvering speeds this will occur well above the speed at which stick-shaker (stall warning) takes place.
Immediate action is to be taken by the pilot when "AIRSPEED LOW" is displayed. It is considered that the airplane is entering the 'approach to stall' phase. Here's an actual extract (maybe not the latest though)
The first indication of an approach to stall is the AIRSPEED LOW EICAS
message. A stall warning should be readily identifiable by the pilot,
either by an artificial indication (stick shaker) or natural
indication (initial buffet). During the initial stages of a stall,
local airflow separation results in buffeting, giving a natural
warning of an approach to stall. Stick shaker operation will usually
precede initial buffet as a stall warning indication. In some cases,
near cruise altitude and cruise Mach, stick shaker may be simultaneous
with initial buffet. Recovery from an approach to stall should be
initiated at the earliest recognizable stall warning, either AIRSPEED
LOW EICAS message, stick shaker or initial buffet.
Thus the procedure is the same for both the AIRSPEED LOW and SS and it is called, "Approach to stall or stall recovery". Here are the first few steps only:
Initiate the recovery:
- Smoothly apply nose down elevator to reduce the angle of attack until buffet or stick shaker stops.
Continue the recovery:
- Roll in the shortest direction to wings level if needed
- Advance thrust levers as needed
- Retract the speedbrakes
note 1. When the AIRSPEED LOW caution first appears, there would be no SS and if there's no adverse bank, the first action would be to advance thrust levers.
note 2. The procedure quoted by @cmp - If that’s the case, they both take the amount of time to recover, though. Max thrust and point the nose down - has now been changed. The increase in thrust is to be made after this initial procedure of reducing the AoA and leveling wings. This is based on the consensus between industry, regulator, professional pilot's groups etc., who made the study of the altitude loss/ ground contact issues during LOC-I (Loss of Control - Inflight) study.
Actual procedures must nevertheless be checked for the aircraft type being flown and as the actual situation may demand, for e.g. 'ground contact is a factor'.