In reference to 8x10 promo photos from old movies, how can one tell the difference btwn a vintage chemical print & a new inkjet copy?

If I'm holding the prints in my hand, it would be easy-RC and fibre papers feel different than inkjet paper. Then, look at the quality of the print itself. Look for grain rather than pixels. Ink still doesn't look as good as silver gelatin. It has come a very long way, but not that far. Also, ink runs if it gets wet (unless the print is sealed). Dropping it in bleach to sepia tone it would result in a real mess.

If I am looking at it on screen, then magnification is your friend. Blow it up and look at the pixels. The inkjet will have distinct blocks. The vintage print would have been scanned, resulting in artifacts and grain itself would be apparent.

One has a glossy finish, the other is ink on paper.

Examine the image with a magnifying glass. An inkjet image will consist of four dots of colored ink making up most pixels. You will see cyan (blue-green), magenta (red-blue) and yellow dye. You will also see black ink. This is the inkjet method CMYK. The K stands for kicker. This is the black needed because the C+M+Y ink should make a black dot but due to imperfections in the dye they don't make a good black so black ink is added. A black & white print made the old fashion way, shows no colors when viewed with a magnifying glass.

If it's an unmounted print, sometimes the imprint on the back will give it away -- old promo photos weren't printed on HP paper, for example. Otherwise, careful examination at 10x magnification will often enable you to tell. Study a variety of pictures of known origin on various papers to learn to recognize the differences. Evenly toned areas are the easiest.