I've noticed that recent Chrome version does not allow me to download the pdf I'm viewing. I had to open it in Firefox. The Chrome browser only allowed me to save it to drive (cloud)
I am a developer but have to deal with questions on this regularly from people's at my company due to the IT department being small.
There is now a bar of 5 icons at the top. The middle icon, "download", saves the PDF.
Edit: Long-pressing each icon will show you small pop-up text for the icon/action.