Wow, your question really drew out a lot of uninformed people.
The age of consent in Ohio is 16. That means that there is nothing illegal about them having consensual sex. The mom may be under the impression that the age of consent is 18 everywhere but she's wrong.
However, if the 20-year-old is in some kind of position of authority over the 16-year-old, sexual contact is illegal and remains that way until she turns 18. That means if the older person is her teacher, coach, scout leader, etc, there could actually be something illegal about them being sexual together.
Let me add that generally speaking, age of consent laws define the legal age at which you can consent. If you have sex with someone under the age of consent, it's rape because even if there is apparent consent there can be no legal consent. If you don't have sex but you engage in some other kind of sexual activity, it's sexual assault or sexual battery for the same reason. So refraining from having sex wouldn't protect you if you don't refrain from all sexual activity; think anything involving private parts.