This is what Matt said above me but Make can also be used not in a physical sense. (Something you can touch in real life),
Like, i'm making arrangements or he's making me mad.
By make you are creating a cause from an action like, pouring mentos in coke will make it go booooshhh up!
By pouring the mentos you create a cause and effect, like making, make is the effect and anything can be the cause.
He punched me - Cause
So I made him cry, - Effect
Made is just a preposition or a small action word that means to "do" something and create an effect or something out of it.
I made a cake, I got a cake.
"I did that" however has no defined effect. It just means you did something.
But make actually brings a product or an EFFECT,
I made that", means you made something and got it as a REWARD or PRIZE for "doing" it. Do just means to perform an action.