The loss of resolution is near always web site specific. I upload Cookie's images as jpg's at 1920 x 1200 pixels to Postimage. That's currently the pixel count for most medium level monitors with a 1.6 x 1 width:height ratio, and such will fill and fit my screen perfectly. That's about 11% of the original camera data, so yes, a tremendous amount of detail is lost. When I view that same image on the Postimage website, it renders at 1165 x 729 pixels. That's 849,285 dots which is still a lot of data.
When linked to other sites, however, these same images are often displayed at even more reduced resolutions. Mostly, I'd guess, the reductions are to save both upload/download time and memory demands as data are routed around the web.
On this site and with my screen, the owl is displayed at 1279 x 800 pixels, and it does not fill my display. Remember, the source image is actually 1920 x 1200.
Right click the owl image and click properties, and one should see exactly what the owl's resolution is on his display. Your forest image is coming up at 640 x 480 on my machine. Go back to the days of 800 x 600 monitors, and this owl would be much too large to view. Dating myself, but I remember a desktop image half this size taking 5+ minutes to render in the first versions of Windows. Now they simply burst onto the screen.
If I go back to Postimage and download the owl, it will come back to me and be saved at its original dimensions.
Full frame images that are 4,500 + pixels wide would take a long time to download and one would have to scroll side to side and up and down to see such in all its radiance. Most e-mail systems today won't handle one of Cookie's full frame images either, and there's little to be gained if its dimensions exceed the size of ones screen and we want to instantly see the big picture.
Running off a high quality print, however, is another deal entirely, as modern printers can squeeze 300 to 600 pixels into a 1-inch long line. At the small end, that's 90,000 pixels in a 1 x 1 inch square. Hence the need for millions and millions of pixels. It's no wonder ones camera gains so much weight with a good day of shooting.
The short answer is: there's not much we can do about it.
Have a good one,