There's a lot going on here that could be unpacked, but the basic answer is:
Most JPEGs are processed, either in-camera or by the "auto" settings of most raw convertors, to be viewed in color. Other information that would be useful in producing a B&W image will be discarded if not needed to make the color JPEG that results from the raw conversion.
If one desaturates a color JPEG, it's not going to look the same as if one had started at the beginning and set white balance, black point, white point, contrast curves, color filters (yes, do you remember when we often used color filters in front of the lens to alter the tonal values of differently colored objects in the scene while shooting B&W film?), etc. in order to produce a B&W image.
B&W film and the way we shoot with it are optimized to produce B&W images. Every step in the process is governed by the fact that the final result will be a monochrome image. The response curves of B&W film to different wavelengths of light are not the same shape as the response curves of each of the three layers in color film. The response curves of B&W film to different wavelengths of light are not the same shape as the sensitivity each photosite on a digital sensor, placed behind a filter that is one of three colors, has to light of different wavelengths.
If we want to make a monochrome image out of a digital image file captured with a Bayer masked color digital sensor that looks like a monochrome image produced using B&W film and chemistry, then we need to adjust the response curves used to convert the linear luminance values measured by each set of photosites behind each of the three colors used in the Bayer mask so that the result emulates responses to various wavelengths of light in the same way B&W film and the photopapers we use to print from B&W film respond to various wavelengths of light. Thus the multipliers used for each set of photosites covered by each of the three different colors used in the Bayer mask will be different for producing a B&W image that looks like an image made using B&W film than the multipliers applied to each set of photosites covered by each of the three different colors used in the Bayer mask for producing a color image. Once the data in the raw file has undergone the process of demosaicing, applying gamma correction, WB multipliers, etc. and has been completed and the result exported to a JPEG, that process is irreversible using only the more limited information contained in the JPEG. Of course we can go back and create a different conversion from the unaltered original raw data, but we need the raw file to do it. The JPEG that was already created using that raw data doesn't contain all of the information we need.
Even if we begin with the raw image data and set the WB correction, color temperature, gamma correction, etc. as they would optimally be set for producing a color image before we simply desaturate it, then we'll get a similar result to the result we'd get by desaturating the color JPEG. If we want to get the result that looks like a B&W photo created using monochromatic film and chemical development, then we must alter all of the processing steps between the raw data collected by the sensor and the image we export to emulate B&W film and chemistry. It's quite possible to do so, but one has to tell the raw development application to do it that way.
How B&W film differs from B&W photo papers
Various B&W films can have different "looks". Some are sensitive only to blue light the way early emulsions spread on glass plates were. Some are orthochromatic and are also sensitive, to one degree or another, to green as well as blue light. Some are panchromatic and sensitive to light across the full visible spectrum including red light.
When we develop panchromatic film, we can not do it under a red safe light! To do so before it is fully developed would fog the film! The film must be developed in total darkness.¹ Once the film has been developed and fixed, there is no longer any color information present and the film is no longer sensitive to any color of light. We can turn all of the lights on, or even go outside into bright sunlight and look at the negatives. They will not change due to their exposure to light. (At least they will not change perceptibly over a short time period. Over longer periods of time the UV light in sunlight would cause the negative to fade, just as long periods of exposure to sunlight will fade many other types of inks, dyes, paint, etc.)
When we decide to make prints, we can go back into the darkroom, shut out all of the external light, and can then use a red safe light if the photo paper we are using to print our images from the negatives is not sensitive to red light. At this point the negative only has varying degrees of density. There's no color information left. So it doesn't matter if we only shine blue light through the negative or if we shine full spectrum light through the negative to expose the photo paper. All of the information contained in the negative can now be printed using only blue light. The paper will only respond to the portion of the light shone through the negative that is blue and, to a lesser degree, green. Any red light that falls on it will not cause a chemical response. That's why a red safe light works in a darkroom.
¹ A very dim green safe light may be used with pan chromatic film for very short periods of time if absolutely necessary, but almost all commercial film processors and even most "DIY" home labs use light tight contraptions to develop film using time and temperature methods without looking at the film using any type of safe light.