Key word: "basically"

Read section 2.4 of the PDF you linked for a bit of additional information on this "bsaically".

GhostScript is a postscript interpreter which can handle PDF files by applying the relatively simple transformations described in that section of the PDF. Whether they embedded the ghostscript exploit within the PDF, or didn't, it's not particularly important for making my point.

That seems like saying "Python is basically a subset of C; just run the simple transformations Cython implements". PDF can be transformed into something a PostScript interpreter can understand in the same way Python can be transformed into something GCC can understand. That is not what "subset" means.

... did you read the bit of the PDF I referenced?

Yes. The section itself says PDF differs significantly from PostScript. The required changes detailed there to transform a PDF to PostScript are substantial: add PostScript implementations of the PDF operators; extract and translate the page content, changing the operator names, decompressing and recompressing text, graphics, and image data, and deleting PDF-only content; translate and insert font data; reorder the content into page order. What you end up with is very different - PDF is not basically just a subset of PostScript.

The substantial differences are in terms of restrictions to postscript to reduce it to a declarative language rather than a full fledged programming language.

A PDF is a collection of isolated, restricted postscript programs (content streams) and the data required for rendering stuffed into one file. The overarching format is a subset of COS. But for all intents and purposes you can imagine this as a tarball containing postscript and other data.

The transformations required to go from PDF to postscript amount to:

1. Include some boilerplate

2. Pull out the content streams (postscript bits) ignoring the pdf-specific extensions

3. Search and replace the names of two procedures

4. Pull out the data required for rendering, optionally decompressing it if your postscript output doesn't support the particular compression in use

5. Concatenate all the data in the right order (on the basis of some metadata in the format)

6. It's now just normal postscript

Fun fact, to top it off: The COS format which is the structure behind a PDF, itself looks a lot like postscript, that's because apparently it's originally based on postscript [0] (although it has deviated).

[0]: https://archive.is/xBd9y (search for postscript)