These are great questions and I hope you don't mind the wall of text that's going to follow. I want to warn anyone reading that the Wikipedia article for the Tanner scale necessarily includes pictures of sexual characteristics at various stages of development, and is therefore NSFW.

Pedophilia is currently defined as primary attraction towards prepubescent children, which are Tanner stage 1, typically age 13 or younger. The DSM-5 and ICD-11 both recognize it as a disorder and have similar, but differing diagnostic criteria.

Hebephilia is defined as primary attraction towards pubescent children, Tanner stages 2 and 3. It's not recognized as a disorder, and there's a lot of debate regarding it in the mental health field. Should it be its own disorder? Should it be considered a subset of pedophilia? Should it just be considered the same as pedophilia? Mental health is a soft science, so these kinds of discussions are how we arrive at diagnostic criteria.

Ephebophilia is defined as primary attraction towards adolescents, Tanner stages 4 and 5, which correspond to about age 15 and older. Attraction to such a person isn't considered disordered as they've developed sexual characteristics which indicate physical adulthood and sexual maturity. This is the imporant distinction that separates it from pedophilia and hebephilia.

The most common age of consent in Europe is 14-16, but I don't think that legality should dictate morality. I think it's great that younger people have the opportunity to engage in sexual conduct with each other, but people much older than they are can easily coerce them, either with charm, money, a sense of authority, etc. An older person who habitually engages in sexual conduct with teenagers and young adults is, in my opinion, targeting them as people who are less powerful and easy to abuse.

I don't think that any sexual abuser is more or less bad than another based on who they're abusing or whether they have a recognized mental disorder. (In fact I would argue that anyone who engages in coersive or forceful sexual practices, including ephebophiles, has something wrong with their brain that makes them be a bad person.) Diagnosis of a disorder can help us understand motivation and develop prevention techniques, but it's not an excuse for harming someone.

There's a hidden implication that Epstien being a pedophile is worse than being an ephebophile, as if raping teenagers is somehow better than raping children. Insisting he is a pedophile plays into and reinforces this idea. I think it's an unhealthy way to view sexual assault, both in how society sees survivors and how survivors see themselves.

I also think that demonizing pedophiles (meaning the term clinically and not people who have abused children) puts more children at risk. If someone feels the need to hide their disorder they're much less likely to seek medical help, warn those around them, and recieve help in preventing harmful behavior. You can see the benefits of destigmatizing mental disorders in things like alcoholism or borderline personality disorder, where people are now much more likely to seek therapy than they were in the past. I would prefer that my neighbor were a non-offending pedophile attending regular treatment than a closeted pedophile who poses a serious risk to those around them. I would want them to reach out to me for help when they feel they're about to harm someone rather than craft secret plans to go through with it. This cannot happen in a world where asking for help can ruin your life.