A pedophile is simply attracted to children. This does mean he/she will act on that attraction. The BBC had an article about celibate pedophiles. These men love children, too much. The idea of abusing a child is abhorrent to them, so they are celibate.

Child rape can also be an expression of control and violence, like any other form of rape. South Africa had (and may still have) an epidemic of child rape. Black men who felt powerless as a result of apartheid and its aftermath often raped women and children because that was something in their power. This is not a racial thing: it happens in other societies. Fathers rape their children, usually, girls because of narcissism and sociopathy. A narcissistic parent regards children as perfect extensions of himself. A sociopath is a sadist by definition. Just look at Trump: he's attracted to Ivanka and speculated about Tiffany's sexual development when she was a baby. A normal father can recognize his daughter's beauty without overriding his paternal instinct to protect her. Trump is not one of these men. Sadism is integral to his immigration policies.