All endotoxins are pyrogens but all pyrogens are not endotoxins

In pharmaceuticals pyrogens and endotoxins are related to bacterial endotoxin testing. These two terms used interchangeably sometimes but the thing is that both have different meanings. So what is the difference? 

Pyrogens are the substances which cause rise in body temperature and induces fever. Pyrogen can be external or internal like any forgein particle when entered in body can act as pyrogen or body's internal molecules can act as pyrogen. So if we look the term pyrogen, it has a wide range which includes forgein particles, internal molecules etc. But endotoxins are released by the cell wall of the gram negative bacteria after cell death. These are basically lipopolysaccharides (LPS) in nature. Endotoxins when gets inside the body also cause rise in temperature and induce fever but endotoxin are one of the category of pyrogens. So all endotoxins are pyrogens but all pyrogens are not endotoxins.