Whiff Cancel allows you to cancel an attack early for the cost of 75% of your Burst meter. Pretty much everything can be whiff cancelled so long as you have the meter to do so. It lets you cancel whichever attack you're doing and allows you to do something else on the following frame.
Free Cancel allows you to cancel an attack whenever you opponent's next opportunity to move is. If either you or the opponent hit each other while selecting Free Cancel, it won't cancel since one of you has been hit. It needs to be on an attack that doesn't hit the opponent. IE: You're +1 and you go for a grab, which is 4 frames. Your opponent can react to the grab with a jump, roll, their own grab, etc. If you free cancel the grab, you could choose to stick with the grab OR do an option to try and beat the opponent's choice. If you think they're going to jump, you could do an attack which would beat the jump. Ninja's Uppercut for example would beat jump or grab from the opponent but still lose to roll.