I want to understand the difference between mining by using hard disks (burst), and renting the empty space of the hard disk (storj). Is what both are based on the cloud storage project?
BURST has you write "plot" files with pre-generated data in very large quantities to your drive, then it searches a specific sub-set of that data every time it is told there is a new block to process for a dataset with the lowest "deadline".
Has nothing at all to do with cloud storage like Storj or Maid at all, and you can't use the potted drive space for anything else.