Pulmonary embolisms create a ventilation-perfusion mismatch that basically amounts to a lot of your lung's surface area for gas exchange being wasted. Because of this, your blood doesn't have enough surface area to properly work with to soak up oxygen I its brief pass through the lungs, as all of your circulation is being fed away from the embolus. CO2 diffuses pretty rapidly across the plasma membrane (20x faster than oxygen) so you can make up for that lack of surface area by merely increasing your ventilation and thus maximizing the difference between alveolar and pulmonary capillary CO2. Oxygen, on the other hand, is sluggish. It needs that surface area to exchange, so until you open up the other side if the pulmonary circulation you will have a serious oxygen exchange problem. This is critical to understand, as it us the very reason that oxygenation and ventilation are handled separately when a patient is on a ventilator, and why you generally intubate or use noninvasive ventilation for ventilation issues, while providing supplementary oxygen or CPAP for oxygenation issues.
Now anemia presents a case of less RBCs, but their exchange of O2 is in no way affected. So they'll grab O2 in the same manner as they always do, and thus your oxygen saturation and PO2 are unchanged. What is changed, however, is total oxygen content- you have less hemoglobin, so regardless of PaO2, you've got less oxygen content in your arterial blood. Your PvO2 and venous oxygen content will also be markedly depleted, as your tissues will deplete a more substantial percentage of your total O2 content, leaving less bound and free oxygen available in your venous blood compared to someone who isn't anemic.
