<< IGraphM`

g1 = Graph[{1 -> 3, 1 -> 4, 1 -> 4, 2 -> 3, 2 -> 3, 2 -> 4}]

g2 = Graph[{1 -> 2, 1 -> 2, 1 -> 3, 2 -> 4, 3 -> 4, 3 -> 4}]

IGIsomorphicQ[g1, g2]
(* False *)

g1 = Graph[{1 <-> 3, 1 <-> 4, 1 <-> 4, 2 <-> 3, 2 <-> 3, 2 <-> 4}]

g2 = Graph[{1 <-> 2, 1 <-> 2, 1 <-> 3, 2 <-> 4, 3 <-> 4, 3 <-> 4}]

IGIsomorphicQ[g1, g2]
(* True *)

IGGetIsomorphism[g1, g2]
(* {<|1 -> 1, 3 -> 3, 4 -> 2, 2 -> 4|>} *)

asc1 = Counts[Sort /@ EdgeList[g1]]
(* <|1 <-> 3 -> 1, 1 <-> 4 -> 2, 2 <-> 3 -> 2, 2 <-> 4 -> 1|> *)

asc2 = Counts[Sort /@ EdgeList[g2]]
(* <|1 <-> 2 -> 2, 1 <-> 3 -> 1, 2 <-> 4 -> 1, 3 <-> 4 -> 2|> *)

IGVF2FindIsomorphisms[{Graph[VertexList[g1],Keys[asc1]], "EdgeColors" -> asc1}, {Graph[VertexList[g2],Keys[asc2]], "EdgeColors" -> asc2}]
(* {<|1 -> 1, 3 -> 3, 4 -> 2, 2 -> 4|>, <|1 -> 3, 3 -> 1, 4 -> 4, 2 -> 2|>,
    <|1 -> 2, 3 -> 4, 4 -> 1, 2 -> 3|>, <|1 -> 4, 3 -> 2, 4 -> 3, 2 -> 1|>} *)