Why LRC NEF file exported to PNG 16bit ProPhoto are not identical?

Please post screenshot that show the difference.

Are you on Windows or Mac, and in what application are you viewing the PNG?

And why are you exporting a 16-bit PNG? The PNG format is designed for web graphics with predominantly solid colors.

If this is a regular photograph, jpg is the preferred format, which will offer much better compression than PNG, with (usually) little quality loss, depending on the Quality setting.

If you intend to edit the exported file in Photoshop, use 16-bit Tiff or PSD. You can then just right click the image in Lightroom and choose Edit in Photoshop, with no need for exporting.

Also note that there is no need to export in ProPhoto because Lightroom uses a variant of ProPhoto as its working space.

Color management will ensure that the image displays correctly in color managed applications, no matter what color space you choose on Export.

And unless you know what you're doing, stay away from ProPhoto, and use Adobe RGB or sRGB instead.

ProPhoto is indtended for editing only, and a ProPhoto file should never leave your computer.

sRGB is the safe choice, especially if the image is going online, or is intended for screen viewing only.

And viewing a ProPhoto file in an application without color management usually leads to desaturation.