The difference is simple;
Trading your Pokemon is when you trade from game-to-game, like when you trade from X/Y to ORAS, or US to UM. The 2 games have to be compatible with each other to trade. For example, a X or Y game cannot trade with a US of UM game, but it can trade with another X or Y game or a ORAS game, and vise-virsa.
Migrating your Pokemon is when you use Pokebank or Poketransporter to transfer your Pokemon from a game that is not compatible with US or UM, and migrate them to that game.
I did this with my friend's Pokemon X game; I took all my Pokemon in X and migrated them to UM.
Hope this answers your question! :)
