Vindictive, revengeful, vengeful are close synonyms often used interchangeably to mean showing or motivated by a desire for vengeance.
Distinctively vindictive tends to stress this reaction as inherent in the nature of the individual and, therefore, is especially applicable when no specific motivating grievance exists.
The term can imply a persistent emotion or a tendency to seek revenge for real or fancied wrongs or slights, sometimes with implacable malevolence, sometimes with spiteful malice, but occasionally it implies no more than a punitive or retributive intent.
Revengeful and vengeful are more likely to suggest the state of one specifically provoked to action and truculently ready to seek revenge.
Additionally revengeful and especially vengeful can apply to an agent or weapon by which vengeance is won.