From the perspective of someone who worked in printing and publishing starting in the 1980s, there's more to it than that. PostScript was and is terrific as a page description language and as a printer control language. It absolutely revolutionized the printing business. For the first time, you could get complete pages (as opposed to unpaginated galleys) out of high-end imagesetters.
But it was not all that good as a way to send documents to be printed elsewhere. Postscript files were in some ways too dependent on the printer they targeted, so the person creating the PS file had to know too much about the printer that would be used to print it: its resolution and optimal halftone screen frequencies, media sizes, etc. With high-resolution output on photographic film costing around $10 per foot, mistakes could be expensive as well as time-wasting.
Fonts could also be a problem. Ideally, the PS file would contain all the fonts it required but this did not fit very well with the terms of most font licenses. And some applications would include a copy of every font used once on each page on which it was used. This was in line with Adobe's recommended Document Structuring Conventions and had the advantage of making pages within the file independent of one another, but for documents with hundreds of pages, this could add up fast and make the PS file literally hundreds of times larger than if all the fonts were included just once. With small storage media and slow network links, this was a real problem.
The "P" in PDF is for portable, and these are the problems it solved. Unlike a PS file, a PDF file is not targeted for a specific printer model, and most font licenses allowed the licensee to include subsetted fonts in PDF files. I personally prepared PS files for a few thousand books to be printed at various places around the US and later, PDF files for thousands more. There is no comparison: PDF was and is better in every way for this purpose.