This may be a better question for a forum of psychiatrists and psychologists. I think your question goes beyond a linguistic one. That said, here's my attempt at an informed answer that has an emphasis on terms used by researchers and clinicians in the mental health field.
A quick search on Google Scholar yielded a term that may be useful to you. You might use the term non-offending pedophile for someone who is sexually attracted to children, but does not molest children. A journal article with that term as a title can be found in Current Sexual Health Reports, September 2016, Volume 8, Issue 3, pp 121-128. You will note that the definition of non-offending includes no molestation of children and no use of illegal media that exploit children.
Offending pedophile would then be the term for a person with sexual attraction for children who does sexually molest children. Colloquially, child molester is a useful term, but it probably does not include pedophiles who use child pornography. Predatory pedophile is a term I came across in my searches and it seems useful as well, as suggested in a previous answer.
There has been a lot of controversy about the definition and categorization of pedophilia in the "Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition" colloquially called the DSM-5, the latest edition of the diagnostic manual of the American Psychiatric Association published in 2013. You can read a good summary here about what the DSM-5 says about pedophilia. Pedophilia is considered a paraphilic disorder.
In DSM-5 the term paraphilia is defined as “any intense and
persistent sexual interest other than sexual interest in genital
stimulation or preparatory fondling with phenotypically normal,
physiologically mature, consenting human partners.” Paraphilias,
however, may not necessarily classify as “intense and persistent” but
rather preferential sexual interests or sexual interests that are
greater than nonparaphilic sexual interests. The addition of the word
“disorder” to the classification of paraphilias is new to DSM-5. (http://www.psychiatrictimes.com/dsm-5-0/dsm-5-and-paraphilias-what-psychiatrists-need-know)
Pedophilic Disorder is a DSM-5 (Diagnostic and Statistical Manual of Mental Disorders, fifth edition), diagnosis assigned to adults ( defined as age 16 and up) who have sexual desire for prepubescent children (American Psychiatric Association, 2013a).Any behavioral expression of Pedophilic Disorder is a criminal offense in the United States, Canada, and Europe, as well as most other places in the world. Some authors differentiate between having deviant desires for children which are ego-dystonic and resisted, causing guilt, shame, and distress, vs. desires which are indulged through fantasy, associating with other pedophiles, possession and trading of pornographic images, or direct observation, self-exposure, or physical contact with a victim (Harvard University, 2010; Vachss, 2013)
If you can wade through the psych jargon, this scholarly article (Arch Sex Behav (2015) 44:1127–1138) gives a good overview of how the change in sexual norms in culture influences mental health and legal ideas of what is pathological or criminal. The move is away from the idea of deviance and toward the idea of consent between adult partners and lack of harm to self and other.