How can a movie from 1987 be better in HD than SD? Does that apply to all movies that were recorded on old-style film?
Because the resolution of film is better than the resolution of standard-definition TV. It is difficult to define the resolution of 'film' since it is not a digital, pixel based media. But film is designed to be sharp even on much larger screens than any television. We can however use the resolution of digital cinema projectors as a good proxy figure.
So to compare the resolutions:
The technology used for Digital Cinema on large movie theatres are called '4k' projectors, and have a resolution of 4096 x 2160 pixels (8.8 megapixels). Smaller screens can use '2k' systems 2048 x 1080 pixels (2.2 megapixels), but the 4k systems are probably the closer proxy to film which can be projected onto very large screens.
Analogue SD TV has a vertical resolution of 480 or 576 interlaced lines. Digital SD also varies in resolution, but the ATSD format is 720 x 480 pixels (under 0.4 megapixels).
Digital HD TV again has several formats, 720p and 1080p are the most common. 1080p has a resolution of 1920 x 1080 pixels (2.1 megapixels) - close to the lower standards of digital cinema projectors currently used.
As you can see from the figures above, the resolution of film exceeds the resolution of SD television by some margin. The resolution of HD TV approaches that of digital cinema.
So a transfer of a movie shot on film to HD TV is going to result in a more faithful copy than than a transfer to SD TV. So a movie shot in the 1980s (or even the 1930s) is going to look better in an HD transfer than an SD one.