All different functions
J, 62 bytes

f=:3 :'~.(2#~2^y)([:&lt;@~.@/:~((i.@!A.i.)y)|:(y#2)$])@#:i.2^2^y'


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-3 bytes for anonymous function (removing f=:)

For each boolean function (truth table), generate its equivalence class, then remove duplicates.