Abduct and kidnap are almost the same thing. The only difference, I think, is a legal difference (and that depends on what the place is and what that place's laws are, so the difference chance from place to place). What I've learned (which might not be true in another place) is that to abduct a person means simply to take them. It's usually a secret. To kidnap a person is to do a special kind of abduction, in which the criminal does not keep it a secret. The stolen person is a "hostage" in exchange for something the criminal wants (money or power, usually). The only case in which the difference is clear is when we talk about stories of aliens stealing people. We call them "alien abductions," not "alien kidnappings." If we aren't talking about aliens or legal cases, the two words are quite interchangeable.

in short: the abductor's goal is to take someone away whereas the kidnapper's goal is to achieve something by abducting someone.

Abduct is to take someone and keep them hidden where only you know where they are. Kidnap is to forcibly remove someone from their daily life, keep them locked up, and then demand a ransom from the family of the person who has been kidnapped.