PDF does not use Postscript, and is not Turing complete. Its drawing model is based on Postscript's (with additions), but its instruction set is focused on drawing, and can't do programming. Here is the instruction set, with equivalent Postscript commands where applicable: https://www.adobe.com/content/dam/acom/en/devnet/pdf/pdfs/PD.... Most parts of the Postscript language have no PDF equivalent.

Other things like JavaScript and Flash can be embedded, but they are extras on top of the document.