Colour Difference between Paste Frame and Background

I tested the two areas with eyedropper in Indesign before exporting it to PDF and both appear to be the same setting of white.

A note on the eyedropper tool, and to clarify my post. It can be used to select and apply color, but isn't a reliable way to determine how color will export or print. Using the eyedropper, you can accurately pick and match color from image objects, but not from placed vector objects like .PDF or .AI files. In those cases the eyedropper picks up the value of the placed vector's RGB preview proxy, and not the actual color values inside of the object.

The Separation Preview panel does predict output values and it would be unusual to get a match there and a mismatch in the exported PDF.

I'm afraid you'll have to provide more detail as to exactly how you're going about this.

What's a "paste frame"? You can't both "place" and "paste" an image.

What are the nature, origin, and color mode of the image?

What is your Transparency Blend Space setting?

What are the intent and settings or your PDF export?

Don't use the eydropper to check the values. With the Separation Preview panel open mouse over the object and check the values in the panel

Colour import/export profiles?