The first synthetic of both words, is Pedo/e which in Greek is Παις = young.
But if you want to push it even further
then
A pedophile is sexually attracted to children.
A pederast has sex with children.
pederasty
Erotic love, sexually expressed or chaste, between a man and an adolescent boy.
(archaic) Anal intercourse in general, usually between a man and an adolescent boy.
Pedophilia
Sexual or erotic feelings or desires directed by adults and late adolescents towards children; particularly, in psychiatry, a paraphilia consisting of a primary adult sexual attraction to prepubescent children.
Sexual acts committed by adults with prepubescent children.
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So in essence, yes they are both acts of pedophilia. BUT, pederasty is specific in that it involves CLEARLY stated act of pedophilia towards "boys". = gay
While pedophilia is a sexual act towards any child girl or boy. Yet not specific. You still deny there is a difference?