What is the difference between "secuestro", "rapto" and "abducción"?

Secuestro y rapto normalmente son utilizados como sinónimos, la principal diferencia radica en que normalmente cuando hay un secuestro es solicitada una suma de dinero y en el rapto no siempre es solicitada.

Secuestrar:

1. Retener indebidamente a una persona para exigir dinero por su rescate, o para otros fines.

Raptar:

1. Secuestrar, retener a alguien en contra de su voluntad, por lo general con el fin de conseguir un rescate.

En el caso de Abducir generalmente es empleado para los supuestos secuestros por parte de seres extraterrestres:

2. Dicho de una supuesta criatura extraterrestre: Apoderarse de alguien.

Secuestro and Rapto are synonyms. They implies to retain people against their will. Often with violence (not only physical). Kindnap would be the right translation into english.

Abducción is the kind of kindnap done by E.T. Here the violence is not so explicit.

We also use abducir (verb instead of subject) to make reference to a strong and powerful attraction.

All three secuestro, abducción and rapto are nouns for the action of verbs secuestrar, abducir and raptar, respectively. Now, as to the difference between these:

Secuestrar means to take by force an individual or a means of transport, and can also be used to refer to judicially seize goods that are either illegal or of which the owner is unclear and to determine.

Abducir is a verb used mainly to refer to supposed extraterrestrial beings taking someone, and also to attract a person powerfully to oneself, rather than taking a person as in English 'Abduct', which is spelled similarly.

Raptar refers only to the forceful or deceitful taking of a person, mainly the case of a man taking a woman.

Secuestro is the most commonly used word if you're referring to the taking of a person; rapto can also be used, but it's not as common.