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.
