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A bronsted acid is a proton donor, and the base is a proton acceptor. A Lewis acid is a lone pair acceptor while the base is a lone pair donor. The "opposite" part is just that the "donor" and "acceptor" titles for acids and bases are the opposite for the two categories.
The difference between Bronsted and Lewis acids and bases is in the way that they describe the actions of an acid and base. The Bronsted definition has to do with proton transfer while the Lewis definition has to do with electron lone pairs.
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