Yes that's correct, to the best of my knowledge.
Yes, Windows ships with something named pscript.dll or similar. That renders PostScript commands from some other format, probably GDI. I'm not sure if it ships with a generic PCL translator as my experience is with PostScript MFDs, but it does ship with some PCL drivers so no doubt those files are available for other drivers to use too.
The GDI is a device independent set of drawing commands. You can use it to draw pictures onto a window, into a .wmf file, or onto a piece of paper via a printer or plotter. It's the same set of commands. A bit like how the same HTML can appear on a computer screen or be printed onto paper, whereas something like PCL is designed for drawing on paper only (there aren't many programs around that will render PCL on the screen for example.)
Some printers can natively speak PCL or PS, and in this case you can take a PostScript or PCL program and send it directly to the printer (with simple tools like "copy file.ps lpt1:") and it will print fully rendered. This is because the PCL/PS code is processed inside the printer itself. This is rather complex, so cheaper printers tend to use simpler solutions like accepting only an image file, requiring the computer (print driver) to do all the rendering and just submitting the final image to the hardware.
Since PCL and PS are owned by various companies, I believe you have to licence it if you want to include it in your printer (not sure about PCL but definitely for PS.) To avoid these expensive licensing fees, some companies have come up with their own PS interpreters that aren't using any licenced code. I guess they can't claim true PS support because they haven't paid the licence fee, so they call it "emulation" instead. From a user point of view there's no difference between genuine PS support and PS emulation, except for very rare circumstances where there's a bug in one PS interpreter and not another. I had an issue once with a Toshiba copier where it would staple documents for you, but because of a bug in its PS "emulation", when printing certain PDF files some of the pages would come out upside down. Normally you could just turn the page around but when the machine had already stapled it for you it looked a bit silly. Printing the same document on a Ricoh copier (with officially licenced PS support, no "emulation") produced the document without any problems.