I have an InDesign document with a transparent Photoshop document on top. When I paste the Photoshop document on the black InDesign background, I get white borders around my transparent objects, but when I put the black background in the Photoshop document I don't get the problem. Anyone who can help me?
Be aware that the InDesign preview mode is faulty at best. To save memory and CPU, InDesign doesn't render a super-high quality preview, even in preview mode and with 'High Quality Display' turned on. Especially things like transparency and blending are among the first things it cuts corners on.
The answer is: there might be no difference, provided the two blacks are identical. It's just that Photoshop puts a lot more effort in rendering the on-screen preview than InDesign does.
To get a better view of what your product is going to be, export a test file from InDesign, be it a .jpg or a digital .pdf (as opposed to a print .pdf). And even then, in case of the .pdf, your pdf viewe may be somewhat faulty.