My understanding is that...
Daisy Staysail: Flies to windward of the spinnaker and tacks some place between the bow and the mast. When I've flown one of these, ours was much lighter than the one in the photo and we only ever carried it in extremely light winds. After researching on the net, apparently it can be used as a windseeker/windfinder/drifter as well.
Windseeker/windfinder/drifter: Flies to windward of the spinnaker and tacks some place between the bow and the mast. Originally I thought this was synonymous with the Daisy I mentioned above. However, the Internet tells me that windseekers will be tacked to the bow and therefore have a luff that is too long to be a Daisy Staysail, although you can fly a Daisy as a windseeker.
Spanker/Blooper: This flies leeward of the spinnaker and is set beside it. I don't believe that fits the picture above, however, I have never flown one so I could be wrong.
Spinnaker Staysail: My understanding is that is an overall/umbrella term to cover the Daisy Staysail, Windseeker/Windfinder/Drifter types of sail. Any sail set within the fore triangle... But I haven't found an article to confirm or refute that.
(As an aside, be careful when Googling "Spanker" at work.)