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I think they're two different acid-base theories; the difference is that a Lewis theory states that an acid is an electron acceptor and a base is an electron donor, and the Bronsted theory states that an acid is a proton donor and a base is a proton acceptor.
I think that a Bronsted definition of acids means that acids require a hydrogen (because a proton H+ needs to be released), whereas a Lewis acid means that some compounds without hydrogen can still be acids in certain reactions.
A bronsted acid is a proton donor. A Lewis acid is the species that accepts the e- pair. So, a Lewis acid is a broad term for anything that accepts a pair of electrons, whereas a bronsted acid is specifically the proton donor.
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