When eggs rot, they putrefy or start to smell really, really bad. Putrefy is to begin stinking, usually when rotting or decomposing.
When you describe something as putrid, it means it is foul or disgusting –– drinking Coke and milk together is gross. Add ketchup, and the cocktail becomes putrid. But technically, putrid, like putrefy, refers to the smell of something organic that has begun to decompose. Open the lid of your garbage can and you will smell the putrefying remains of your meals. Both putrid and putrefy share the Latin root of putr which you can remember by its first two letters — P. U.!