"Throw something on the floor" is usually used in more of an expressive than literal context. Usually, when you "throw something on the floor", you're not actually throwing it, you're dropping it casually, or maybe tossing it. Sometimes we might also use the expression to indicate we did something quickly: I threw on some clothes, throw dinner on the stove, etc. This does not mean that "throw on the floor" is never used literally ("during his tantrum, he threw all his food on the floor"). However, throwing at is generally used in a more literal sense, and usually indicates deliberateness and/or force.