I am confident that the exact method used by each camera manufacturer is different and company-confidential. All manufacturers have a large vested interest in getting the maximum image quality using methods that are undetectable and therefore not reproducible by their competition.

In the case of Nikon, several sources describe a simple subtraction; for instance: https://improvephotography.com/48889/long-exposure-noise-reduction-use/

Dark frame subtraction occurs when that reference file, the dark frame, is used to subtract the hot pixels from the image file that includes both the signal and noise, which is the photo you intended to capture, plus the resulting noise.

And also: https://www.nikonians.org/reviews/understanding-long-exposure-noise-reduction

When you enable Long Exposure NR and an exposure is longer than one second (eight seconds on older Nikon DSLRs), the camera will take two pictures with approximately the same exposure time for each. The first picture is normal. The second picture is a black-frame subtraction exposure, which is exposed for about the same duration as the first picture, but with the shutter closed.

The camera examines the noise in the black-frame subtraction exposure and subtracts it from the first, normal image.

I am unaware of any in-camera long exposure noise reduction (LENR) that uses a more sophisticated process, although exact methodologies may be and probably are proprietary and confidential.

Because astrophotography sometimes requires stacking many images, dozens or even hundreds, perhaps, it is usually preferable to take all the exposures without LENR and take a few dark frames at the end. The dark frame(s) can then be subtracted in software during post-processing. As well, sophisticated processing, noise reduction, despeckling, etc., can then be applied and compared as desired.