I believe I can help a little, at least on reading the datasheets.
The first L in your specifications refers to distance (length) of detection.
in the parenthesis, such as (HLS) the data is indicating an output voltage level change. HLS indicates a transition from High to Low. LHL would indicate a transition from Low to High. At 5 volt Vcc this would be 5 volts to 0 volts and vice versa. Or, perhaps more correctly, the transition "threshold" voltages where the logic level is considered to be high or low.
The S and L at the end would (I think) indicate short range detection versus long range detection.
LHL would indicate the distance at which the detector no longer picks up the reflected signal because it is too far away. LHS would be the closest point at which a detection output transition can occur.
Now, it would appear after reviewing one of these datasheets that the output switching characteristics are quanitified by both the reflective object moving toward the detector and the reflective object moving away from the detector. In other words, the distance at which the output switches would not be the same for both cases. You might say there is a bit of hysterisis in the response. In the datasheet I looked at, the output goes low when the reflective surface is detected, and is high when the surface is not detected. There is a distance that is too close where the focal performance of the source will not be adequate to be picked up when reflected. This would be the "S" indication at the end. Then there is a distance that is too far, which would be the "L" indication at the end. The distance inbetween is the "detecting distance" where the reflective surface will properly reflect the optical source to the detector. This would be your operating distance, and the LHS, HLS, HLL, and LHL distances can be understood and accounted for as the reflective object moves in and out of the operating zone of the "detecting distance".
So, as the object moves away from a point too close to the detector, the output will be high. At a certain distance, the reflective surface will be in the "detection region" and the output will transition L(HLS) to a low state. In the detection region, the low state will be maintained. When the end of the detection region is approached, the output will transition back to the high state L(LHL) and will maintain that state as long as the reflective surface is beyond this distance. As the reflective object changes direction and approaches the detector, the L(HLL) transition to low will occur, and will maintain low as long as the reflective surface is in the detection region. As it moves closer, to the point of being too close again, it will go high again L(LHS) and stay high as long as it is too close. Once it reaches the point once again of the detection region, L (HLS) will occur and the output will once again be low.
Again, the H to L and L to H distances are not the same for an approach or a wayward movement. There is a shift so to speak.
I hope this is clear.