Answer:
The difference originally was that "on" commenced adjectival phrases and "upon" commenced adverbial ones. Thus, "the vase is on the table", since "on the table" describes the position of the vase, but "I placed the vase upon the table", since "upon the table" describes the action of placing.
This was a pretty subtle difference, which led to people using the terms interchangeably and eventually not using the word "upon" any more except in poetry (the extra syllable sometimes helped the rhythm) or in specific phrases. You will almost never hear it nowadays.