Difference Between a Child molester and a Pedophile
A pedophile can be a paraphilia, especially if he maintains his urges as mere fantasy. They can fantasize and masturbate to the thoughts or ask their partners to wear child's costumes. It can be hard, but with self-control, a pedophile can live all their lives without abusing children.
While a child abuser has evil thoughts and consciously or deliberately commits the act, the abuser could be a pedophile, but there's no difference between a child molester that abuses children and a rapist that rapes an adult. They are both sexual predators.
Just being a pedophile is not illegal in any way since there are ways you can satisfy your urges that don't involve a child. It could be sex with dolls and mannequins designed as children, or sex with child-like adults, and role-playing (dressed in school uniforms and as a toddler with immature talks). Some of the most popular porn sites have categories like "high school students and teacher," "step-dad and daughters," and many other role-playing categories. So don't be quick stigmatize people who identify as pedophiles because a significant number of them have never abused a child before.
To be realistic, many child abusers are pedophiles. However, they are not the same. A child abuser could be hebephilia or act out of the desire to dominate, for vengeance, past experiences. There are situations where people deliberately molest the children of their ex-spouse to get back at them; the list goes on. These abusers cause both mental and physical harm to children, but the mere fantasy of a pedophile is not harmful to anyone.