Why are attached images...
 

...downloaded so much more than attached thumbnails?

If I attach a thumbnail to a thread it is often downloaded less than a hundred times and in the same amount of time an attached image is downloaded over a thousand times.

Who is downloading these images and where to?

Because anyone who opens that page (including spiders and bots that are crawling the net) are literally downloading the image, whereas if you attach an image as a thumbnail, then it is only downloaded if one follows its link (otherwise, only the thumbnail is). As for the destination of the download, it's in whatever directory the browser cache is kept.

Aaaaaah I see - thank you for that

What does the count mean?
 

The downloaded count in the attachments is the number of times the attachment is accessed, or 'saved' by someone or some process?

It's the same thing. If someone or something "accesses" an attachment, for example by clicking on it, the file is already saved in their browser cache, whether they click "save" or not, and so it counts as one download.