I am not always in agreement with terms used by some translators, and that's always a problem with translation.
You could say that Buddhists believe in sin if you to use the root definition that sin is to miss the mark or err rather than to offend a god figure or break a dogmatic rule. So, using the word sin would be misleading to some and a better word would be more useful and correct in a modern context. Delusion and ignorance are far more useful and applicable here.
You could easily say that Buddhism involves salvation, and the term is used as part of the Buddha's, (Sakyamuni) last words to his followers. Yet, there is no actual mediator, and rather than salvation from a moralistically defined, dualistic evil, it is purely a salvation from the bondage of ignorance and suffering itself. We are implicitly, all Buddhas.
In my understanding a Buddha is a teacher who provides methods to realize one's own True Nature. The result is not aimed at a religious reward as a goal, like an eternal life in a Heaven plane.
Buddha does not judge and sentence people to any plane of existence as a reward or punishment. Instead it is our actions and the law of cause and effect that are what bring whatever mind states result during life or death, as you may well know.
It is probably a good idea not to argue with people who are using similar words in a different context when they are not aware of the various meanings and relationships involved and how context influences meaning.
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