Like most other terms used in psychiatry and politics, the meaning appears to be self-evident, but it's actually wrong.  Other examples include "insane," "antisocial" (it means criminal), and "inflammable." ("Inflammable means flammable?  What a country!") 

Pedophile had originally been divided into two groups, fixated and regressed.  Interestingly, even these terms don't mean what they look like they mean.  They don't describe what kind of kid the pedophile likes; they describe why he is a pedophile.

Fixated pedophiles are fixed in a certain developmental stage, and are exclusively attracted to kids. 

Regressed pedophiles, using the original definition, prefer adults but, if stressed, will regress to an earlier developmental stage; this regression leads them to prefer children.   The regressed pedophile likes kids because he himself has "become" a kid (more technically: he regresses to a pregenital sexuality, which finds its satisfaction in oral  (e.g. masturbation, fetishism) or anal impulses (e.g. sadomasochism) and its natural compatriot, the child.) 

The terms homosexual and heterosexual apply to the primary object choice, not necessarily the sex of the victim (e.g. "heterosexual molester of boys.")  Fixated pedophiles tend to be (i.e. think of themselves as)  homosexual, and regressed (think of themselves as) heterosexual.

But the easiest way, and most forensically  useful way, is to simply describe pedophiles according to their sexual object preference: Fixated pedophiles are true pedophiles, they are only sexually aroused by kids.  Opportunistic (regressed) pedophiles would rather have a hot 25 year old, but will take the best offer.  Regressed pedophiles don't think they are pedophiles. 

Remember, whether they are homosexual or not isn't the differentiating factor (e.g. male homosexual regressed pedophiles prefer adult men but would settle for a kid.  Heterosexual fixated pedophiles prefer kids.)

An example of the fantasy life of each is illustrative: the fixated pedophile might be married, but will take a feature of the adult and "see" it as child like.  Maybe the slope of the calf, the hair style, etc.  Fetishism is also important, and there is a clear (to the pedophile, not to anyone else) direct link to children (a type of cloth or pattern; sounds such as bells, crowds; language or words, etc.)

The regressed, or opportunistic, pedophile does the opposite: "I know she's only 13, but have you seen her ass?!" 

So now you can see why all of our attempts at catching pedophiles before they offend are doomed to absolute failure: they're everywhere.  I know no one will admit this, but remember how hot you thought Britney Spears was in the original video "Hit Me Baby One More Time?"  Guess what.  You're a pedophile.  You say, "but I'd never act on it."  Well, you say a lot of things.

But that's the crux, of course: desire and action are very different things, and, arguably are controlled by entirely different parts of the brain, or personality factors, or superego departments.  Not a day goes by I don't want to plasma gun 50 people I meet.  But, so far body count = 0.  This is why we can only be judged on our behaviors, not our thoughts (though a person must judge himself on his thoughts.)

You don't know what a person is capable of until they are presented with the temptation, so I'm saying we shouldn't tempt them.  The problem with opportunistic pedophilia is that it is opportunistic, not pedophilia.  The goal isn't the child; it's ejaculation.  And you simply don't know where a person's "line in the sand" for ejaculation is.  At what point do they say, "this is probably not right?"  Not: "this is wrong,"  that's usually easy to describe.  Probably wrong.  16?  14 if they're famous? 12 if you're in Thailand?

The guy on the IM or chat who gets a 14 year old girl to meet him at the pier-- he's a "regressed pedophile."  He would have liked her to have been a 25 year old NFL cheerleader; but, let's face it, a 25 year old NFL cheerleader would sooner swallow her own eye than hook up with this freak, and he knows it.  So he bypasses her ("they're all sluts") and cons a 14 year old.  It's no surprise that  75% of heterosexual pedophiles described their offenses as "compensation." 

Fixated pedophiles are sometimes described as "child centered."  In fact, they see themselves as the peers of the child, and prefer to interact with the child on its level (while regressed pedophiles try to elevate the interaction with the kid to adult level.)  They're not in it "for the sex" but for the emotional connection.  For the regressed, the sex is the whole point.  And here's your forensic problem: a regressed pedophile kidnaps a kid to have sex with.  Once done, well, anything can happen.  If the kid "liked it," (maybe defined as "didn't put up too much of a fight") there's a good chance they'll meet again.  But if the kid didn't like it...  A fixated pedophile kidnaps a kid to-- live with.  That fantasy rarely gets realized (kid likely doesn't want to move in) and violence can therefore occur.  But appreciate the difference: for a regressed pedophile, the violence is part of the offense.  For the fixated, violence is secondary or utilitarian.

I can already hear the screaming objections.  Look, I'm not trying to defend anyone, I'm trying to explain the offenses, the thinking.  In simple terms, your child is a billion times more at risk from "pedophilia" with an adult they know (30% of victims have known their attacker for a full year prior to the offense), who is already married with kids of his own that he has not molested, then they are from the registered pedophile who lives in your city who was hoarding child porn in his mom's basement.  I know it sounds cooler and more self-righteous to rail against the pedophile than to worry about your (weak-minded) social contacts, because you think you know them, and especially since they outnumber you.  By a lot.

You say, "but certainly not everyone is a pedophile, there must be something specifically different about them?" Or, if you work for the Supreme Court: "there must be some mental abnormality which is properly the domain of medicine?"

No.  Not in a way that's useful.  For example, a very recent MRI study of fixated pedophiles vs. controls found pedophiles had decreases in grey matter (smaller brains), especially in certain brain regions (orbitofrontal, ventral striatum, limbic regions), and generally decreased intelligence.  But before you see this as proof that pedophilia finds its origins in brain biology, the physical brain changes didn't predict anything you might expect (number of offenses, psychopathy, etc)-- but it did predict obsessiveness.   In other words, this study found biological evidence of OCD spectrum pathology, but not of pedophilia, per se.  No, pedophilia isn't a disease with distinct physical pathology, and no, it isn't properly the domain of psychiatry.

I may write a "profile" of the pedophilic sex offender, and another post reviewing the developmental and biological studies so far.  Or, I may just go have a drink (or 4.)