I'm not familiar with either term specifically, but I would guess that an opinion essay might only have to include your personal opinion on the subject, which presumably only gives one viewpoint. In an argumentative essay, I guess you are expected to show two (or more) sides of an argument and then perhaps come to a conclusion at the end. That would be the same for a "for and against" essay. A "for and against" essay about bullfighting, for example, would give both the view supporting it and also arguments for it to be banned.
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