So, is the first image in your original post the actual screenshot at full size, the last one a screenshot of what you see in the PDF from InDesign?
The original screenshot looks fine for what it is, a screenshot (I think that screenshots should usually represent what you'd see on screen).
I think the problems you're seeing are down to your Display Performance settings (switching to High Quality should improve that), and more importantly, your PDF Export Settings are downsampling your screenshots. In the Export Adobe PDF dialog box, navigate to Compression, and try setting everything to 'Do Not Downsample'. This is presuming your images are all screenshots, and there's no large photographic images or anything that might bloat your PDF. You might want to play with the compression settings to see what yields your preferred balance of quality and file size.