PDF is an Acronym for Portable Document Format. Invented by Adobe.

PDF is an open standard. You can generate PDFs using Adobe's commercial AdobeAcrobat and view them with AcrobatReader (free but not Free). You can use LaTeX (pdflatex(1) or LaTeXpdf are good places to look) to make good quality PDF files. xpdf(1) and GhostView are Free programs that you can use to view PDF files if you don't want to use Adobe's closed-source reader.

PostScript files can be easily turned into PDF with the ps2pdf(1) command (which is a wrapper around GhostScript).

Apple's MacOSX uses PDF for rendering images (and the user interface), which is why you can have true transparent windows on their OS.

PDF is arguably a version of PostScript and is certainly a decendant of it in some ways. Calling PDF something other than PostScript II was probably actually a very good idea, since there are already enough different forms of PostScript around.