The word Epitaph is a noun, and it is a phrase or words that are written in memory of someone who has passed away. Mostly it is used on a tombstone to commemorate a person's life. Sometimes it is depicted in the form of one of the deceased's favorite sayings or something that is personal to them.
However, the Epithet is simply a descriptive word or phrase that is usually joined and associated with a name like "William the Conqueror." In today's world, the epithet is often used disparagingly. An Epithet is also used to identify species, variety, and other subunits within a genus.