They are different but they are all nutrients. Living thins need nitrogen, phosphorus and carbon to thrive. Many take much of their carbon from photosynthesis but still need some organic carbon.
An organic is a molecule that contains a hydrogen and a carbon atom. Many contain a vast array of other things including nitrogen , phosphorous and metals. Organics include theings like fats, ammino acids, proteins ,vitamins and toxins. They are generally hydrophobic( repelled by water) ; some are amphipathic ( drawn to water at one end and repelled at the other. The later are most susceptible to skimming as the molecule gets trapped in the air water interface and foamed out.
Inorganic phosphate( PO4 species) and inorganic nitrogen( ammonia, nitite, nitrate) bind stongly to the water and are not removable by a skimmer.
Many organics breakdown and release inorganic nitrogen and phosphate. Some organics are more refractory than others and resist breaking down. Exporting dissoved and particulate organics before they release inorganic nitrogen and phosphorous is why aquarists use skimming, granulated activated carbon and some resins to help nitrae and phospahte levels by getting at them before they are realeased by the organic molecules.