I think fiat money is easily understood. Lawful money is more difficult since it isn't defined anywhere. However, it clear that it is not just gold and silver coin or US Treasury notes redeemable in the same. It is a class of money broader than legal tender. Milam v. U.S in 1974 ruled that Federal Reserve Notes were lawful money.
I think you mixed it up. Lawful money is easily understood as it is defined somewhere, 371 4/16 grain pure silver (24.1 grams). However fiat money (Federal Reserve Note) is more difficult to understand as it isn't defined anywhere.