How are Lewis acids and bases distinguished from others?
They are "distinguished" from other (older definition) acids and bases by their donation or acceptance of electrons, rather than by the formation of hydrogen ions.
The expansion from the Arrhenius acid-base theory to a more general understanding of proton transfer explained the acid/base behavior of many more compounds than the previous inorganic water-based systems.
In the Lewis theory of acid-base reactions, bases donate pairs of electrons and acids accept pairs of electrons. A Lewis acid is therefore any substance, such as the H+ ion, that can accept a pair of nonbonding electrons. In other words, a Lewis acid is an electron-pair acceptor. A Lewis base is any substance, such as the OH- ion, that can donate a pair of nonbonding electrons. A Lewis base is therefore an electron-pair donor.