Some have asked if oxygen deprivation masks work the same way that BFR belts do in producing hypoxia and then, if so, is that what is producing performance improvements from both technologies.  The quick answer is that “No, they work in completely different ways” and while proof is lacking that oxygen deprivation masks improve performance, there is robust data showing BFR training does improve strength and fitness.
Oxygen deprivation masks or rebreathing systems attempt to reduce the oxygen getting into the body through the lungs.  This is seen as some as a way to “train at altitude or in hypoxia” while at sea level.  First, hypoxic training has NOT been shown to improve sea level strength or endurance performance.  Second, by restricting breathing, one may get some gains in respiratory muscle strength, but there is little to no influence on SpO2 so that working muscle has near normal oxygen levels available for work.  It is not hypoxic, unlike exercising at altitude or BFR training.
Now regarding hypoxic training (either by exercising at altitudes above 6000 ft or by breathing hypoxic gas mixtures), the SpO2 may be reduced from 95-100% to 85% to 90%.  The whole body (importantly including brain, heart and muscle) is exposed to this reduced oxygen in the arteries (hypoxemia).  The net effect of a reduced SpO2 is that less work is performed and heart and brain are stressed to a greater extent.  However, the actual amount of oxygen delivered to working muscle is not very different from normal sea level training.  So due to near normal delivery of oxygen and reduced work performed, the SmO2 (saturation of hemoglobin in muscle) is not very different from normal (perhaps, dropping from 40% to 30%) and there is little disturbance of homeostasis in working muscle.  In summary, whole body hypoxic training does reduce oxygen in the blood (SpO2), but oxygen delivery to and concentrations in working muscle (SmO2) is only slightly reduced.
When performing BFR training properly, there is a profound reduction in oxygen in the muscle.  Normally, at rest, SpO2 is ~98%, while hemoglobin in muscle is ~70% saturated with oxygen (SmO2 = 70%).  When exercising maximally, at sea level, SmO2 may drop to ~40%.  With BFR training, SpO2 remains high (95-100%), while oxygen in muscle may drop to less than 10% (SmO2 ~ 10%) as blood flow to the working muscle is restricted.  Exercising muscle uses oxygen that must be replaced for the muscle to keep working and to maintain homeostasis.  When that resupply of oxygen is restricted, the muscle becomes very hypoxic (SmO2 < 10%) and a metabolic crisis ensues stimulating local processes to reverse the situation.  This disturbance of homeostasis is sensed by the brain and in response, releases hormones to facilitate improvement of oxygen transport in the body.
So, in summary, oxygen deprivation masks, hypoxic training and BFR training are all very different techniques, working through different mechanisms, with very different results.
Oxygen deprivation masks make breathing harder, perhaps, improving respiratory strength.Hypoxic training somewhat reduces oxygen in the arterial blood, but minimally impacts the oxygen delivered and used in working muscle.  The brain is the organ most sensitive to a reduction in oxygen delivery and adjusts behavior accordingly.Proper BFR training does not reduce the oxygen in arterial blood, but severely limits oxygen resupplying working muscle, producing profound hypoxia and acidosis in working muscle, while maintaining oxygen delivery to heart and brain.  The profound hypoxia and acidosis, stimulate robust anabolic processes to improve strength, performance and fitness.I